TSTP Solution File: ANA009-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 1.71s 1.90s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 9 unt; 0 nHn; 7 RR)
% Number of literals : 18 ( 2 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)
| ~ c_lesse_quals(B,C,A)
| c_lesse_quals(c_plus(B,D,A),c_plus(C,D,A),A) ),
file('ANA009-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Oab__group__add(A)
| c_plus(B,c_uminus(B,A),A) = c_0 ),
file('ANA009-2.p',unknown),
[] ).
cnf(3,axiom,
~ c_lesse_quals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b),
file('ANA009-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) ),
file('ANA009-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Oab__group__add(A) ),
file('ANA009-2.p',unknown),
[] ).
cnf(7,axiom,
c_lesse_quals(v_lb(A),v_f(A),t_b),
file('ANA009-2.p',unknown),
[] ).
cnf(8,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA009-2.p',unknown),
[] ).
cnf(9,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(hyper,[status(thm)],[8,5]),
[iquote('hyper,8,5')] ).
cnf(10,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(hyper,[status(thm)],[8,4]),
[iquote('hyper,8,4')] ).
cnf(11,plain,
c_plus(A,c_uminus(A,t_b),t_b) = c_0,
inference(hyper,[status(thm)],[9,2]),
[iquote('hyper,9,2')] ).
cnf(13,plain,
c_lesse_quals(c_plus(v_lb(A),B,t_b),c_plus(v_f(A),B,t_b),t_b),
inference(hyper,[status(thm)],[7,1,10]),
[iquote('hyper,7,1,10')] ).
cnf(17,plain,
c_lesse_quals(c_0,c_plus(v_f(A),c_uminus(v_lb(A),t_b),t_b),t_b),
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1,11.1.1')] ).
cnf(18,plain,
$false,
inference(binary,[status(thm)],[17,3]),
[iquote('binary,17.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n029.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 : 300
% 0.12/0.34 % DateTime : Wed Jul 27 10:10:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.71/1.90 ----- Otter 3.3f, August 2004 -----
% 1.71/1.90 The process was started by sandbox on n029.cluster.edu,
% 1.71/1.90 Wed Jul 27 10:10:29 2022
% 1.71/1.90 The command was "./otter". The process ID is 21663.
% 1.71/1.90
% 1.71/1.90 set(prolog_style_variables).
% 1.71/1.90 set(auto).
% 1.71/1.90 dependent: set(auto1).
% 1.71/1.90 dependent: set(process_input).
% 1.71/1.90 dependent: clear(print_kept).
% 1.71/1.90 dependent: clear(print_new_demod).
% 1.71/1.90 dependent: clear(print_back_demod).
% 1.71/1.90 dependent: clear(print_back_sub).
% 1.71/1.90 dependent: set(control_memory).
% 1.71/1.90 dependent: assign(max_mem, 12000).
% 1.71/1.90 dependent: assign(pick_given_ratio, 4).
% 1.71/1.90 dependent: assign(stats_level, 1).
% 1.71/1.90 dependent: assign(max_seconds, 10800).
% 1.71/1.90 clear(print_given).
% 1.71/1.90
% 1.71/1.90 list(usable).
% 1.71/1.90 0 [] A=A.
% 1.71/1.90 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)| -c_lesse_quals(V_a,V_b,T_a)|c_lesse_quals(c_plus(V_a,V_c,T_a),c_plus(V_b,V_c,T_a),T_a).
% 1.71/1.90 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_plus(V_a,c_uminus(V_a,T_a),T_a)=c_0.
% 1.71/1.90 0 [] c_lesse_quals(v_lb(V_U),v_f(V_U),t_b).
% 1.71/1.90 0 [] -c_lesse_quals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b).
% 1.71/1.90 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T).
% 1.71/1.90 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Oab__group__add(T).
% 1.71/1.90 0 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.71/1.90 end_of_list.
% 1.71/1.90
% 1.71/1.90 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.71/1.90
% 1.71/1.90 This is a Horn set with equality. The strategy will be
% 1.71/1.90 Knuth-Bendix and hyper_res, with positive clauses in
% 1.71/1.90 sos and nonpositive clauses in usable.
% 1.71/1.90
% 1.71/1.90 dependent: set(knuth_bendix).
% 1.71/1.90 dependent: set(anl_eq).
% 1.71/1.90 dependent: set(para_from).
% 1.71/1.90 dependent: set(para_into).
% 1.71/1.90 dependent: clear(para_from_right).
% 1.71/1.90 dependent: clear(para_into_right).
% 1.71/1.90 dependent: set(para_from_vars).
% 1.71/1.90 dependent: set(eq_units_both_ways).
% 1.71/1.90 dependent: set(dynamic_demod_all).
% 1.71/1.90 dependent: set(dynamic_demod).
% 1.71/1.90 dependent: set(order_eq).
% 1.71/1.90 dependent: set(back_demod).
% 1.71/1.90 dependent: set(lrpo).
% 1.71/1.90 dependent: set(hyper_res).
% 1.71/1.90 dependent: clear(order_hyper).
% 1.71/1.90
% 1.71/1.90 ------------> process usable:
% 1.71/1.90 ** KEPT (pick-wt=16): 1 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)| -c_lesse_quals(B,C,A)|c_lesse_quals(c_plus(B,D,A),c_plus(C,D,A),A).
% 1.71/1.90 ** KEPT (pick-wt=10): 2 [] -class_OrderedGroup_Oab__group__add(A)|c_plus(B,c_uminus(B,A),A)=c_0.
% 1.71/1.90 ** KEPT (pick-wt=11): 3 [] -c_lesse_quals(c_0,c_plus(v_f(v_x),c_uminus(v_lb(v_x),t_b),t_b),t_b).
% 1.71/1.90 ** KEPT (pick-wt=4): 4 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A).
% 1.71/1.90 ** KEPT (pick-wt=4): 5 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Oab__group__add(A).
% 1.71/1.90
% 1.71/1.90 ------------> process sos:
% 1.71/1.90 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.71/1.90 ** KEPT (pick-wt=6): 7 [] c_lesse_quals(v_lb(A),v_f(A),t_b).
% 1.71/1.90 ** KEPT (pick-wt=2): 8 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.71/1.90 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.71/1.90
% 1.71/1.90 ======= end of input processing =======
% 1.71/1.90
% 1.71/1.90 =========== start of search ===========
% 1.71/1.90
% 1.71/1.90 -------- PROOF --------
% 1.71/1.90
% 1.71/1.90 ----> UNIT CONFLICT at 0.00 sec ----> 18 [binary,17.1,3.1] $F.
% 1.71/1.90
% 1.71/1.90 Length of proof is 5. Level of proof is 3.
% 1.71/1.90
% 1.71/1.90 ---------------- PROOF ----------------
% 1.71/1.90 % SZS status Unsatisfiable
% 1.71/1.90 % SZS output start Refutation
% See solution above
% 1.71/1.90 ------------ end of proof -------------
% 1.71/1.90
% 1.71/1.90
% 1.71/1.90 Search stopped by max_proofs option.
% 1.71/1.90
% 1.71/1.90
% 1.71/1.90 Search stopped by max_proofs option.
% 1.71/1.90
% 1.71/1.90 ============ end of search ============
% 1.71/1.90
% 1.71/1.90 -------------- statistics -------------
% 1.71/1.90 clauses given 7
% 1.71/1.90 clauses generated 12
% 1.71/1.90 clauses kept 16
% 1.71/1.90 clauses forward subsumed 5
% 1.71/1.90 clauses back subsumed 0
% 1.71/1.90 Kbytes malloced 976
% 1.71/1.90
% 1.71/1.90 ----------- times (seconds) -----------
% 1.71/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.90 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.71/1.90
% 1.71/1.90 That finishes the proof of the theorem.
% 1.71/1.90
% 1.71/1.90 Process 21663 finished Wed Jul 27 10:10:31 2022
% 1.71/1.90 Otter interrupted
% 1.71/1.90 PROOF FOUND
%------------------------------------------------------------------------------