TSTP Solution File: ANA017-2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA017-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 12:46:43 EDT 2022
% Result : Unsatisfiable 1.68s 1.90s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 13 unt; 0 nHn; 12 RR)
% Number of literals : 29 ( 4 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_lesse_quals(c_HOL_Oabs(c_times(v_c,v_b(v_x(A)),t_b),t_b),c_times(A,c_HOL_Oabs(v_f(v_x(A)),t_b),t_b),t_b),
file('ANA017-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| c_lesse_quals(c_0,c_HOL_Oabs(B,A),A) ),
file('ANA017-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_OrderedGroup_Osemigroup__mult(A)
| c_times(c_times(B,C,A),D,A) = c_times(B,c_times(C,D,A),A) ),
file('ANA017-2.p',unknown),
[] ).
cnf(4,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('ANA017-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Opordered__semiring(A)
| ~ c_lesse_quals(B,C,A)
| ~ c_lesse_quals(c_0,D,A)
| c_lesse_quals(c_times(D,B,A),c_times(D,C,A),A) ),
file('ANA017-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Osemigroup__mult(A) ),
file('ANA017-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Ring__and__Field_Opordered__semiring(A) ),
file('ANA017-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Olordered__ab__group__abs(A) ),
file('ANA017-2.p',unknown),
[] ).
cnf(10,axiom,
c_lesse_quals(c_HOL_Oabs(v_b(A),t_b),c_times(v_ca,c_HOL_Oabs(v_f(A),t_b),t_b),t_b),
file('ANA017-2.p',unknown),
[] ).
cnf(11,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA017-2.p',unknown),
[] ).
cnf(12,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(hyper,[status(thm)],[11,8]),
[iquote('hyper,11,8')] ).
cnf(13,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(hyper,[status(thm)],[11,7]),
[iquote('hyper,11,7')] ).
cnf(14,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(hyper,[status(thm)],[11,6]),
[iquote('hyper,11,6')] ).
cnf(16,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)],[11,4]),
[iquote('hyper,11,4')] ).
cnf(17,plain,
~ c_lesse_quals(c_times(c_HOL_Oabs(v_c,t_b),c_HOL_Oabs(v_b(v_x(A)),t_b),t_b),c_times(A,c_HOL_Oabs(v_f(v_x(A)),t_b),t_b),t_b),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),16]),
[iquote('back_demod,1,demod,16')] ).
cnf(18,plain,
c_lesse_quals(c_0,c_HOL_Oabs(A,t_b),t_b),
inference(hyper,[status(thm)],[12,2]),
[iquote('hyper,12,2')] ).
cnf(19,plain,
c_times(c_times(A,B,t_b),C,t_b) = c_times(A,c_times(B,C,t_b),t_b),
inference(hyper,[status(thm)],[14,3]),
[iquote('hyper,14,3')] ).
cnf(22,plain,
c_lesse_quals(c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(v_b(B),t_b),t_b),c_times(c_HOL_Oabs(A,t_b),c_times(v_ca,c_HOL_Oabs(v_f(B),t_b),t_b),t_b),t_b),
inference(hyper,[status(thm)],[18,5,13,10]),
[iquote('hyper,18,5,13,10')] ).
cnf(33,plain,
~ c_lesse_quals(c_times(c_HOL_Oabs(v_c,t_b),c_HOL_Oabs(v_b(v_x(c_times(A,B,t_b))),t_b),t_b),c_times(A,c_times(B,c_HOL_Oabs(v_f(v_x(c_times(A,B,t_b))),t_b),t_b),t_b),t_b),
inference(para_from,[status(thm),theory(equality)],[19,17]),
[iquote('para_from,19.1.1,17.1.2')] ).
cnf(34,plain,
$false,
inference(binary,[status(thm)],[33,22]),
[iquote('binary,33.1,22.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA017-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.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 09:57:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.90 ----- Otter 3.3f, August 2004 -----
% 1.68/1.90 The process was started by sandbox on n004.cluster.edu,
% 1.68/1.90 Wed Jul 27 09:57:06 2022
% 1.68/1.90 The command was "./otter". The process ID is 27824.
% 1.68/1.90
% 1.68/1.90 set(prolog_style_variables).
% 1.68/1.90 set(auto).
% 1.68/1.90 dependent: set(auto1).
% 1.68/1.90 dependent: set(process_input).
% 1.68/1.90 dependent: clear(print_kept).
% 1.68/1.90 dependent: clear(print_new_demod).
% 1.68/1.90 dependent: clear(print_back_demod).
% 1.68/1.90 dependent: clear(print_back_sub).
% 1.68/1.90 dependent: set(control_memory).
% 1.68/1.90 dependent: assign(max_mem, 12000).
% 1.68/1.90 dependent: assign(pick_given_ratio, 4).
% 1.68/1.90 dependent: assign(stats_level, 1).
% 1.68/1.90 dependent: assign(max_seconds, 10800).
% 1.68/1.90 clear(print_given).
% 1.68/1.90
% 1.68/1.90 list(usable).
% 1.68/1.90 0 [] A=A.
% 1.68/1.90 0 [] c_lesse_quals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b).
% 1.68/1.90 0 [] -c_lesse_quals(c_HOL_Oabs(c_times(v_c,v_b(v_x(V_U)),t_b),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b).
% 1.68/1.90 0 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.68/1.90 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_lesse_quals(c_0,c_HOL_Oabs(V_a,T_a),T_a).
% 1.68/1.90 0 [] -class_OrderedGroup_Osemigroup__mult(T_a)|c_times(c_times(V_a,V_b,T_a),V_c,T_a)=c_times(V_a,c_times(V_b,V_c,T_a),T_a).
% 1.68/1.90 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).
% 1.68/1.90 0 [] -class_Ring__and__Field_Opordered__semiring(T_a)| -c_lesse_quals(V_a,V_b,T_a)| -c_lesse_quals(c_0,V_c,T_a)|c_lesse_quals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a).
% 1.68/1.90 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Osemigroup__mult(T).
% 1.68/1.90 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Ring__and__Field_Opordered__semiring(T).
% 1.68/1.90 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Olordered__ab__group__abs(T).
% 1.68/1.90 end_of_list.
% 1.68/1.90
% 1.68/1.90 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.68/1.90
% 1.68/1.90 This is a Horn set with equality. The strategy will be
% 1.68/1.90 Knuth-Bendix and hyper_res, with positive clauses in
% 1.68/1.90 sos and nonpositive clauses in usable.
% 1.68/1.90
% 1.68/1.90 dependent: set(knuth_bendix).
% 1.68/1.90 dependent: set(anl_eq).
% 1.68/1.90 dependent: set(para_from).
% 1.68/1.90 dependent: set(para_into).
% 1.68/1.90 dependent: clear(para_from_right).
% 1.68/1.90 dependent: clear(para_into_right).
% 1.68/1.90 dependent: set(para_from_vars).
% 1.68/1.90 dependent: set(eq_units_both_ways).
% 1.68/1.90 dependent: set(dynamic_demod_all).
% 1.68/1.90 dependent: set(dynamic_demod).
% 1.68/1.90 dependent: set(order_eq).
% 1.68/1.90 dependent: set(back_demod).
% 1.68/1.90 dependent: set(lrpo).
% 1.68/1.90 dependent: set(hyper_res).
% 1.68/1.90 dependent: clear(order_hyper).
% 1.68/1.90
% 1.68/1.90 ------------> process usable:
% 1.68/1.90 ** KEPT (pick-wt=18): 1 [] -c_lesse_quals(c_HOL_Oabs(c_times(v_c,v_b(v_x(A)),t_b),t_b),c_times(A,c_HOL_Oabs(v_f(v_x(A)),t_b),t_b),t_b).
% 1.68/1.90 ** KEPT (pick-wt=8): 2 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_lesse_quals(c_0,c_HOL_Oabs(B,A),A).
% 1.68/1.90 ** KEPT (pick-wt=17): 3 [] -class_OrderedGroup_Osemigroup__mult(A)|c_times(c_times(B,C,A),D,A)=c_times(B,c_times(C,D,A),A).
% 1.68/1.90 ** KEPT (pick-wt=17): 4 [] -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).
% 1.68/1.90 ** KEPT (pick-wt=20): 5 [] -class_Ring__and__Field_Opordered__semiring(A)| -c_lesse_quals(B,C,A)| -c_lesse_quals(c_0,D,A)|c_lesse_quals(c_times(D,B,A),c_times(D,C,A),A).
% 1.68/1.90 ** KEPT (pick-wt=4): 6 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Osemigroup__mult(A).
% 1.68/1.90 ** KEPT (pick-wt=4): 7 [] -class_Ring__and__Field_Oordered__idom(A)|class_Ring__and__Field_Opordered__semiring(A).
% 1.68/1.90 ** KEPT (pick-wt=4): 8 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.68/1.90
% 1.68/1.90 ------------> process sos:
% 1.68/1.90 ** KEPT (pick-wt=3): 9 [] A=A.
% 1.68/1.90 ** KEPT (pick-wt=13): 10 [] c_lesse_quals(c_HOL_Oabs(v_b(A),t_b),c_times(v_ca,c_HOL_Oabs(v_f(A),t_b),t_b),t_b).
% 1.68/1.90 ** KEPT (pick-wt=2): 11 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.68/1.90 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 1.68/1.90
% 1.68/1.90 ======= end of input processing =======
% 1.68/1.90
% 1.68/1.90 =========== start of search ===========
% 1.68/1.90
% 1.68/1.90 -------- PROOF --------
% 1.68/1.90
% 1.68/1.90 ----> UNIT CONFLICT at 0.00 sec ----> 34 [binary,33.1,22.1] $F.
% 1.68/1.90
% 1.68/1.90 Length of proof is 9. Level of proof is 3.
% 1.68/1.90
% 1.68/1.90 ---------------- PROOF ----------------
% 1.68/1.90 % SZS status Unsatisfiable
% 1.68/1.90 % SZS output start Refutation
% See solution above
% 1.68/1.90 ------------ end of proof -------------
% 1.68/1.90
% 1.68/1.90
% 1.68/1.90 Search stopped by max_proofs option.
% 1.68/1.90
% 1.68/1.90
% 1.68/1.90 Search stopped by max_proofs option.
% 1.68/1.90
% 1.68/1.90 ============ end of search ============
% 1.68/1.90
% 1.68/1.90 -------------- statistics -------------
% 1.68/1.90 clauses given 12
% 1.68/1.90 clauses generated 41
% 1.68/1.90 clauses kept 31
% 1.68/1.90 clauses forward subsumed 23
% 1.68/1.90 clauses back subsumed 2
% 1.68/1.90 Kbytes malloced 976
% 1.68/1.90
% 1.68/1.90 ----------- times (seconds) -----------
% 1.68/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.90 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.68/1.90
% 1.68/1.90 That finishes the proof of the theorem.
% 1.68/1.90
% 1.68/1.90 Process 27824 finished Wed Jul 27 09:57:07 2022
% 1.68/1.90 Otter interrupted
% 1.68/1.90 PROOF FOUND
%------------------------------------------------------------------------------