TSTP Solution File: ANA015-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA015-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 1.93s 2.14s
% Output : Refutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of clauses : 24 ( 15 unt; 0 nHn; 16 RR)
% Number of literals : 35 ( 4 equ; 14 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 31 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| c_lesse_quals(c_0,c_HOL_Oabs(B,A),A) ),
file('ANA015-2.p',unknown),
[] ).
cnf(2,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('ANA015-2.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('ANA015-2.p',unknown),
[] ).
cnf(4,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('ANA015-2.p',unknown),
[] ).
cnf(5,axiom,
~ c_lesse_quals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(A)),t_a),t_a),c_times(A,c_HOL_Oabs(v_f(v_x(A)),t_a),t_a),t_a),
file('ANA015-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Ofield(A)
| class_OrderedGroup_Osemigroup__mult(A) ),
file('ANA015-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__field(A)
| class_Ring__and__Field_Ofield(A) ),
file('ANA015-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__field(A)
| class_Ring__and__Field_Oordered__idom(A) ),
file('ANA015-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__field(A)
| class_Ring__and__Field_Opordered__semiring(A) ),
file('ANA015-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ class_Ring__and__Field_Oordered__field(A)
| class_OrderedGroup_Olordered__ab__group__abs(A) ),
file('ANA015-2.p',unknown),
[] ).
cnf(12,axiom,
c_lesse_quals(c_HOL_Oabs(v_g(A),t_a),c_times(v_d,c_HOL_Oabs(v_f(A),t_a),t_a),t_a),
file('ANA015-2.p',unknown),
[] ).
cnf(13,axiom,
class_Ring__and__Field_Oordered__field(t_a),
file('ANA015-2.p',unknown),
[] ).
cnf(14,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(hyper,[status(thm)],[13,10]),
[iquote('hyper,13,10')] ).
cnf(15,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(hyper,[status(thm)],[13,9]),
[iquote('hyper,13,9')] ).
cnf(16,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(hyper,[status(thm)],[13,8]),
[iquote('hyper,13,8')] ).
cnf(17,plain,
class_Ring__and__Field_Ofield(t_a),
inference(hyper,[status(thm)],[13,7]),
[iquote('hyper,13,7')] ).
cnf(18,plain,
c_lesse_quals(c_0,c_HOL_Oabs(A,t_a),t_a),
inference(hyper,[status(thm)],[14,1]),
[iquote('hyper,14,1')] ).
cnf(20,plain,
c_HOL_Oabs(c_times(A,B,t_a),t_a) = c_times(c_HOL_Oabs(A,t_a),c_HOL_Oabs(B,t_a),t_a),
inference(hyper,[status(thm)],[16,3]),
[iquote('hyper,16,3')] ).
cnf(21,plain,
~ c_lesse_quals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),c_HOL_Oabs(v_g(v_x(A)),t_a),t_a),c_times(A,c_HOL_Oabs(v_f(v_x(A)),t_a),t_a),t_a),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[5]),20]),
[iquote('back_demod,5,demod,20')] ).
cnf(22,plain,
class_OrderedGroup_Osemigroup__mult(t_a),
inference(hyper,[status(thm)],[17,6]),
[iquote('hyper,17,6')] ).
cnf(23,plain,
c_times(c_times(A,B,t_a),C,t_a) = c_times(A,c_times(B,C,t_a),t_a),
inference(hyper,[status(thm)],[22,2]),
[iquote('hyper,22,2')] ).
cnf(26,plain,
c_lesse_quals(c_times(c_HOL_Oabs(A,t_a),c_HOL_Oabs(v_g(B),t_a),t_a),c_times(c_HOL_Oabs(A,t_a),c_times(v_d,c_HOL_Oabs(v_f(B),t_a),t_a),t_a),t_a),
inference(hyper,[status(thm)],[18,4,15,12]),
[iquote('hyper,18,4,15,12')] ).
cnf(43,plain,
~ c_lesse_quals(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),c_HOL_Oabs(v_g(v_x(c_times(A,B,t_a))),t_a),t_a),c_times(A,c_times(B,c_HOL_Oabs(v_f(v_x(c_times(A,B,t_a))),t_a),t_a),t_a),t_a),
inference(para_into,[status(thm),theory(equality)],[21,23]),
[iquote('para_into,21.1.2,23.1.1')] ).
cnf(44,plain,
$false,
inference(binary,[status(thm)],[43,26]),
[iquote('binary,43.1,26.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA015-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 10:04:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.93/2.14 ----- Otter 3.3f, August 2004 -----
% 1.93/2.14 The process was started by sandbox2 on n020.cluster.edu,
% 1.93/2.14 Wed Jul 27 10:04:23 2022
% 1.93/2.14 The command was "./otter". The process ID is 7708.
% 1.93/2.14
% 1.93/2.14 set(prolog_style_variables).
% 1.93/2.14 set(auto).
% 1.93/2.14 dependent: set(auto1).
% 1.93/2.14 dependent: set(process_input).
% 1.93/2.14 dependent: clear(print_kept).
% 1.93/2.14 dependent: clear(print_new_demod).
% 1.93/2.14 dependent: clear(print_back_demod).
% 1.93/2.14 dependent: clear(print_back_sub).
% 1.93/2.14 dependent: set(control_memory).
% 1.93/2.14 dependent: assign(max_mem, 12000).
% 1.93/2.14 dependent: assign(pick_given_ratio, 4).
% 1.93/2.14 dependent: assign(stats_level, 1).
% 1.93/2.14 dependent: assign(max_seconds, 10800).
% 1.93/2.14 clear(print_given).
% 1.93/2.14
% 1.93/2.14 list(usable).
% 1.93/2.14 0 [] A=A.
% 1.93/2.14 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_lesse_quals(c_0,c_HOL_Oabs(V_a,T_a),T_a).
% 1.93/2.14 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).
% 1.93/2.14 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).
% 1.93/2.14 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).
% 1.93/2.14 0 [] c_lesse_quals(c_HOL_Oabs(v_g(V_U),t_a),c_times(v_d,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a).
% 1.93/2.14 0 [] -c_lesse_quals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(V_U)),t_a),t_a),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_a),t_a),t_a).
% 1.93/2.14 0 [] -class_Ring__and__Field_Ofield(T)|class_OrderedGroup_Osemigroup__mult(T).
% 1.93/2.14 0 [] -class_Ring__and__Field_Oordered__field(T)|class_Ring__and__Field_Ofield(T).
% 1.93/2.14 0 [] -class_Ring__and__Field_Oordered__field(T)|class_Ring__and__Field_Oordered__idom(T).
% 1.93/2.14 0 [] -class_Ring__and__Field_Oordered__field(T)|class_Ring__and__Field_Opordered__semiring(T).
% 1.93/2.14 0 [] -class_Ring__and__Field_Oordered__field(T)|class_OrderedGroup_Olordered__ab__group__abs(T).
% 1.93/2.14 0 [] class_Ring__and__Field_Oordered__field(t_a).
% 1.93/2.14 end_of_list.
% 1.93/2.14
% 1.93/2.14 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.93/2.14
% 1.93/2.14 This is a Horn set with equality. The strategy will be
% 1.93/2.14 Knuth-Bendix and hyper_res, with positive clauses in
% 1.93/2.14 sos and nonpositive clauses in usable.
% 1.93/2.14
% 1.93/2.14 dependent: set(knuth_bendix).
% 1.93/2.14 dependent: set(anl_eq).
% 1.93/2.14 dependent: set(para_from).
% 1.93/2.14 dependent: set(para_into).
% 1.93/2.14 dependent: clear(para_from_right).
% 1.93/2.14 dependent: clear(para_into_right).
% 1.93/2.14 dependent: set(para_from_vars).
% 1.93/2.14 dependent: set(eq_units_both_ways).
% 1.93/2.14 dependent: set(dynamic_demod_all).
% 1.93/2.14 dependent: set(dynamic_demod).
% 1.93/2.14 dependent: set(order_eq).
% 1.93/2.14 dependent: set(back_demod).
% 1.93/2.14 dependent: set(lrpo).
% 1.93/2.14 dependent: set(hyper_res).
% 1.93/2.14 dependent: clear(order_hyper).
% 1.93/2.14
% 1.93/2.14 ------------> process usable:
% 1.93/2.14 ** KEPT (pick-wt=8): 1 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_lesse_quals(c_0,c_HOL_Oabs(B,A),A).
% 1.93/2.14 ** KEPT (pick-wt=17): 2 [] -class_OrderedGroup_Osemigroup__mult(A)|c_times(c_times(B,C,A),D,A)=c_times(B,c_times(C,D,A),A).
% 1.93/2.14 ** 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).
% 1.93/2.14 ** KEPT (pick-wt=20): 4 [] -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).
% 1.93/2.14 ** KEPT (pick-wt=20): 5 [] -c_lesse_quals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(A)),t_a),t_a),c_times(A,c_HOL_Oabs(v_f(v_x(A)),t_a),t_a),t_a).
% 1.93/2.14 ** KEPT (pick-wt=4): 6 [] -class_Ring__and__Field_Ofield(A)|class_OrderedGroup_Osemigroup__mult(A).
% 1.93/2.14 ** KEPT (pick-wt=4): 7 [] -class_Ring__and__Field_Oordered__field(A)|class_Ring__and__Field_Ofield(A).
% 1.93/2.14 ** KEPT (pick-wt=4): 8 [] -class_Ring__and__Field_Oordered__field(A)|class_Ring__and__Field_Oordered__idom(A).
% 1.93/2.14 ** KEPT (pick-wt=4): 9 [] -class_Ring__and__Field_Oordered__field(A)|class_Ring__and__Field_Opordered__semiring(A).
% 1.93/2.14 ** KEPT (pick-wt=4): 10 [] -class_Ring__and__Field_Oordered__field(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.93/2.14
% 1.93/2.14 ------------> process sos:
% 1.93/2.14 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.93/2.14 ** KEPT (pick-wt=13): 12 [] c_lesse_quals(c_HOL_Oabs(v_g(A),t_a),c_times(v_d,c_HOL_Oabs(v_f(A),t_a),t_a),t_a).
% 1.93/2.14 ** KEPT (pick-wt=2): 13 [] class_Ring__and__Field_Oordered__field(t_a).
% 1.93/2.14 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.93/2.14
% 1.93/2.14 ======= end of input processing =======
% 1.93/2.14
% 1.93/2.14 =========== start of search ===========
% 1.93/2.14
% 1.93/2.14 -------- PROOF --------
% 1.93/2.14
% 1.93/2.14 ----> UNIT CONFLICT at 0.00 sec ----> 44 [binary,43.1,26.1] $F.
% 1.93/2.14
% 1.93/2.14 Length of proof is 11. Level of proof is 4.
% 1.93/2.14
% 1.93/2.14 ---------------- PROOF ----------------
% 1.93/2.14 % SZS status Unsatisfiable
% 1.93/2.14 % SZS output start Refutation
% See solution above
% 1.93/2.14 ------------ end of proof -------------
% 1.93/2.14
% 1.93/2.14
% 1.93/2.14 Search stopped by max_proofs option.
% 1.93/2.14
% 1.93/2.14
% 1.93/2.14 Search stopped by max_proofs option.
% 1.93/2.14
% 1.93/2.14 ============ end of search ============
% 1.93/2.14
% 1.93/2.14 -------------- statistics -------------
% 1.93/2.14 clauses given 16
% 1.93/2.14 clauses generated 64
% 1.93/2.14 clauses kept 41
% 1.93/2.14 clauses forward subsumed 38
% 1.93/2.14 clauses back subsumed 1
% 1.93/2.14 Kbytes malloced 1953
% 1.93/2.14
% 1.93/2.14 ----------- times (seconds) -----------
% 1.93/2.14 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.93/2.14
% 1.93/2.14 That finishes the proof of the theorem.
% 1.93/2.14
% 1.93/2.14 Process 7708 finished Wed Jul 27 10:04:25 2022
% 1.93/2.14 Otter interrupted
% 1.93/2.14 PROOF FOUND
%------------------------------------------------------------------------------