TSTP Solution File: ANA020-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA020-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 1.92s 2.10s
% Output : Refutation 1.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of clauses : 22 ( 15 unt; 0 nHn; 19 RR)
% Number of literals : 32 ( 4 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 14 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_lesse_quals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('ANA020-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| c_HOL_Oabs(c_0,A) = c_0 ),
file('ANA020-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| c_lesse_quals(c_0,c_HOL_Oabs(B,A),A) ),
file('ANA020-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Orderings_Oorder(A)
| ~ c_less(B,C,A)
| c_lesse_quals(B,C,A) ),
file('ANA020-2.p',unknown),
[] ).
cnf(5,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('ANA020-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Ring__and__Field_Opordered__cancel__semiring(A) ),
file('ANA020-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Orderings_Oorder(A) ),
file('ANA020-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Olordered__ab__group__abs(A) ),
file('ANA020-2.p',unknown),
[] ).
cnf(11,axiom,
v_f(c_0) = c_0,
file('ANA020-2.p',unknown),
[] ).
cnf(12,axiom,
c_less(c_0,v_c,t_a),
file('ANA020-2.p',unknown),
[] ).
cnf(14,axiom,
v_x = c_0,
file('ANA020-2.p',unknown),
[] ).
cnf(15,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file('ANA020-2.p',unknown),
[] ).
cnf(16,plain,
~ c_lesse_quals(c_HOL_Oabs(c_0,t_a),c_times(v_c,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),14,11,14]),
[iquote('back_demod,1,demod,14,11,14')] ).
cnf(17,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(hyper,[status(thm)],[15,8]),
[iquote('hyper,15,8')] ).
cnf(18,plain,
class_Orderings_Oorder(t_a),
inference(hyper,[status(thm)],[15,7]),
[iquote('hyper,15,7')] ).
cnf(19,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(hyper,[status(thm)],[15,6]),
[iquote('hyper,15,6')] ).
cnf(20,plain,
c_lesse_quals(c_0,c_HOL_Oabs(A,t_a),t_a),
inference(hyper,[status(thm)],[17,3]),
[iquote('hyper,17,3')] ).
cnf(22,plain,
c_HOL_Oabs(c_0,t_a) = c_0,
inference(hyper,[status(thm)],[17,2]),
[iquote('hyper,17,2')] ).
cnf(23,plain,
~ c_lesse_quals(c_0,c_times(v_c,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),22]),
[iquote('back_demod,16,demod,22')] ).
cnf(24,plain,
c_lesse_quals(c_0,v_c,t_a),
inference(hyper,[status(thm)],[12,4,18]),
[iquote('hyper,12,4,18')] ).
cnf(29,plain,
c_lesse_quals(c_0,c_times(v_c,c_HOL_Oabs(A,t_a),t_a),t_a),
inference(hyper,[status(thm)],[20,5,19,24]),
[iquote('hyper,20,5,19,24')] ).
cnf(30,plain,
$false,
inference(binary,[status(thm)],[29,23]),
[iquote('binary,29.1,23.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ANA020-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n026.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 10:15:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.92/2.10 ----- Otter 3.3f, August 2004 -----
% 1.92/2.10 The process was started by sandbox on n026.cluster.edu,
% 1.92/2.10 Wed Jul 27 10:15:54 2022
% 1.92/2.10 The command was "./otter". The process ID is 17858.
% 1.92/2.10
% 1.92/2.10 set(prolog_style_variables).
% 1.92/2.10 set(auto).
% 1.92/2.10 dependent: set(auto1).
% 1.92/2.10 dependent: set(process_input).
% 1.92/2.10 dependent: clear(print_kept).
% 1.92/2.10 dependent: clear(print_new_demod).
% 1.92/2.10 dependent: clear(print_back_demod).
% 1.92/2.10 dependent: clear(print_back_sub).
% 1.92/2.10 dependent: set(control_memory).
% 1.92/2.10 dependent: assign(max_mem, 12000).
% 1.92/2.10 dependent: assign(pick_given_ratio, 4).
% 1.92/2.10 dependent: assign(stats_level, 1).
% 1.92/2.10 dependent: assign(max_seconds, 10800).
% 1.92/2.10 clear(print_given).
% 1.92/2.10
% 1.92/2.10 list(usable).
% 1.92/2.10 0 [] A=A.
% 1.92/2.10 0 [] v_f(c_0)=c_0.
% 1.92/2.10 0 [] c_less(c_0,v_c,t_a).
% 1.92/2.10 0 [] v_x=c_0.
% 1.92/2.10 0 [] -c_lesse_quals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a).
% 1.92/2.10 0 [] class_Ring__and__Field_Oordered__idom(t_a).
% 1.92/2.10 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_HOL_Oabs(c_0,T_a)=c_0.
% 1.92/2.10 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_lesse_quals(c_0,c_HOL_Oabs(V_a,T_a),T_a).
% 1.92/2.10 0 [] -class_Orderings_Oorder(T_a)| -c_less(V_x,V_y,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 1.92/2.10 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).
% 1.92/2.10 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Ring__and__Field_Opordered__cancel__semiring(T).
% 1.92/2.10 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Orderings_Oorder(T).
% 1.92/2.10 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Olordered__ab__group__abs(T).
% 1.92/2.10 end_of_list.
% 1.92/2.10
% 1.92/2.10 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.92/2.10
% 1.92/2.10 This is a Horn set with equality. The strategy will be
% 1.92/2.10 Knuth-Bendix and hyper_res, with positive clauses in
% 1.92/2.10 sos and nonpositive clauses in usable.
% 1.92/2.10
% 1.92/2.10 dependent: set(knuth_bendix).
% 1.92/2.10 dependent: set(anl_eq).
% 1.92/2.10 dependent: set(para_from).
% 1.92/2.10 dependent: set(para_into).
% 1.92/2.10 dependent: clear(para_from_right).
% 1.92/2.10 dependent: clear(para_into_right).
% 1.92/2.10 dependent: set(para_from_vars).
% 1.92/2.10 dependent: set(eq_units_both_ways).
% 1.92/2.10 dependent: set(dynamic_demod_all).
% 1.92/2.10 dependent: set(dynamic_demod).
% 1.92/2.10 dependent: set(order_eq).
% 1.92/2.10 dependent: set(back_demod).
% 1.92/2.10 dependent: set(lrpo).
% 1.92/2.10 dependent: set(hyper_res).
% 1.92/2.10 dependent: clear(order_hyper).
% 1.92/2.10
% 1.92/2.10 ------------> process usable:
% 1.92/2.10 ** KEPT (pick-wt=13): 1 [] -c_lesse_quals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a).
% 1.92/2.10 ** KEPT (pick-wt=7): 2 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_HOL_Oabs(c_0,A)=c_0.
% 1.92/2.10 ** KEPT (pick-wt=8): 3 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_lesse_quals(c_0,c_HOL_Oabs(B,A),A).
% 1.92/2.10 ** KEPT (pick-wt=10): 4 [] -class_Orderings_Oorder(A)| -c_less(B,C,A)|c_lesse_quals(B,C,A).
% 1.92/2.10 ** KEPT (pick-wt=17): 5 [] -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).
% 1.92/2.10 ** KEPT (pick-wt=4): 6 [] -class_Ring__and__Field_Oordered__idom(A)|class_Ring__and__Field_Opordered__cancel__semiring(A).
% 1.92/2.10 ** KEPT (pick-wt=4): 7 [] -class_Ring__and__Field_Oordered__idom(A)|class_Orderings_Oorder(A).
% 1.92/2.10 ** KEPT (pick-wt=4): 8 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.92/2.10
% 1.92/2.10 ------------> process sos:
% 1.92/2.10 ** KEPT (pick-wt=3): 9 [] A=A.
% 1.92/2.10 ** KEPT (pick-wt=4): 10 [] v_f(c_0)=c_0.
% 1.92/2.10 ---> New Demodulator: 11 [new_demod,10] v_f(c_0)=c_0.
% 1.92/2.10 ** KEPT (pick-wt=4): 12 [] c_less(c_0,v_c,t_a).
% 1.92/2.10 ** KEPT (pick-wt=3): 13 [] v_x=c_0.
% 1.92/2.10 ---> New Demodulator: 14 [new_demod,13] v_x=c_0.
% 1.92/2.10 ** KEPT (pick-wt=2): 15 [] class_Ring__and__Field_Oordered__idom(t_a).
% 1.92/2.10 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] A=A.
% 1.92/2.10 >>>> Starting back demodulation with 11.
% 1.92/2.10 >>>> Starting back demodulation with 14.
% 1.92/2.10 >> back demodulating 1 with 14.
% 1.92/2.10
% 1.92/2.10 ======= end of input processing =======
% 1.92/2.10
% 1.92/2.10 =========== start of search ===========
% 1.92/2.10
% 1.92/2.10 -------- PROOF --------
% 1.92/2.10
% 1.92/2.10 ----> UNIT CONFLICT at 0.00 sec ----> 30 [binary,29.1,23.1] $F.
% 1.92/2.10
% 1.92/2.10 Length of proof is 9. Level of proof is 3.
% 1.92/2.10
% 1.92/2.10 ---------------- PROOF ----------------
% 1.92/2.10 % SZS status Unsatisfiable
% 1.92/2.10 % SZS output start Refutation
% See solution above
% 1.92/2.10 ------------ end of proof -------------
% 1.92/2.10
% 1.92/2.10
% 1.92/2.10 Search stopped by max_proofs option.
% 1.92/2.10
% 1.92/2.10
% 1.92/2.10 Search stopped by max_proofs option.
% 1.92/2.10
% 1.92/2.10 ============ end of search ============
% 1.92/2.10
% 1.92/2.10 -------------- statistics -------------
% 1.92/2.10 clauses given 11
% 1.92/2.10 clauses generated 20
% 1.92/2.10 clauses kept 26
% 1.92/2.10 clauses forward subsumed 10
% 1.92/2.10 clauses back subsumed 0
% 1.92/2.10 Kbytes malloced 976
% 1.92/2.10
% 1.92/2.10 ----------- times (seconds) -----------
% 1.92/2.10 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.92/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.92/2.10
% 1.92/2.10 That finishes the proof of the theorem.
% 1.92/2.10
% 1.92/2.10 Process 17858 finished Wed Jul 27 10:15:56 2022
% 1.92/2.10 Otter interrupted
% 1.92/2.10 PROOF FOUND
%------------------------------------------------------------------------------