TSTP Solution File: ANA031-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA031-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 12:46:46 EDT 2022
% Result : Unsatisfiable 1.71s 1.91s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of clauses : 23 ( 15 unt; 0 nHn; 13 RR)
% Number of literals : 33 ( 5 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 33 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_lesse_quals(c_times(c_HOL_Oabs(v_b(v_x(A)),t_b),c_HOL_Oabs(v_f(v_x(A)),t_b),t_b),c_times(A,c_times(c_HOL_Oabs(v_f(v_x(A)),t_b),c_HOL_Oabs(v_g(v_x(A)),t_b),t_b),t_b),t_b),
file('ANA031-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| c_lesse_quals(c_0,c_HOL_Oabs(B,A),A) ),
file('ANA031-2.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('ANA031-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(A)
| c_times(B,C,A) = c_times(C,B,A) ),
file('ANA031-2.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('ANA031-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Oab__semigroup__mult(A) ),
file('ANA031-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Osemigroup__mult(A) ),
file('ANA031-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Ring__and__Field_Opordered__semiring(A) ),
file('ANA031-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Olordered__ab__group__abs(A) ),
file('ANA031-2.p',unknown),
[] ).
cnf(11,axiom,
c_lesse_quals(c_HOL_Oabs(v_b(A),t_b),c_times(v_c,c_HOL_Oabs(v_g(A),t_b),t_b),t_b),
file('ANA031-2.p',unknown),
[] ).
cnf(12,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA031-2.p',unknown),
[] ).
cnf(13,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(hyper,[status(thm)],[12,9]),
[iquote('hyper,12,9')] ).
cnf(14,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(hyper,[status(thm)],[12,8]),
[iquote('hyper,12,8')] ).
cnf(15,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(hyper,[status(thm)],[12,7]),
[iquote('hyper,12,7')] ).
cnf(16,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(hyper,[status(thm)],[12,6]),
[iquote('hyper,12,6')] ).
cnf(17,plain,
c_lesse_quals(c_0,c_HOL_Oabs(A,t_b),t_b),
inference(hyper,[status(thm)],[13,2]),
[iquote('hyper,13,2')] ).
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)],[15,3]),
[iquote('hyper,15,3')] ).
cnf(21,plain,
c_times(A,B,t_b) = c_times(B,A,t_b),
inference(hyper,[status(thm)],[16,4]),
[iquote('hyper,16,4')] ).
cnf(23,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_c,c_HOL_Oabs(v_g(B),t_b),t_b),t_b),t_b),
inference(hyper,[status(thm)],[17,5,14,11]),
[iquote('hyper,17,5,14,11')] ).
cnf(34,plain,
c_times(A,c_times(B,C,t_b),t_b) = c_times(B,c_times(A,C,t_b),t_b),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,21]),19]),
[iquote('para_into,18.1.1.1,21.1.1,demod,19')] ).
cnf(44,plain,
~ c_lesse_quals(c_times(c_HOL_Oabs(v_b(v_x(A)),t_b),c_HOL_Oabs(v_f(v_x(A)),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x(A)),t_b),c_times(A,c_HOL_Oabs(v_g(v_x(A)),t_b),t_b),t_b),t_b),
inference(para_from,[status(thm),theory(equality)],[34,1]),
[iquote('para_from,34.1.1,1.1.2')] ).
cnf(84,plain,
c_lesse_quals(c_times(c_HOL_Oabs(v_b(A),t_b),c_HOL_Oabs(B,t_b),t_b),c_times(c_HOL_Oabs(B,t_b),c_times(v_c,c_HOL_Oabs(v_g(A),t_b),t_b),t_b),t_b),
inference(para_into,[status(thm),theory(equality)],[23,21]),
[iquote('para_into,23.1.1,21.1.1')] ).
cnf(85,plain,
$false,
inference(binary,[status(thm)],[84,44]),
[iquote('binary,84.1,44.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA031-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 10:01:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.90 ----- Otter 3.3f, August 2004 -----
% 1.71/1.90 The process was started by sandbox2 on n014.cluster.edu,
% 1.71/1.90 Wed Jul 27 10:01:54 2022
% 1.71/1.90 The command was "./otter". The process ID is 16986.
% 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 [] c_lesse_quals(c_HOL_Oabs(v_b(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b).
% 1.71/1.90 0 [] -c_lesse_quals(c_times(c_HOL_Oabs(v_b(v_x(V_U)),t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_f(v_x(V_U)),t_b),c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),t_b).
% 1.71/1.90 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_lesse_quals(c_0,c_HOL_Oabs(V_a,T_a),T_a).
% 1.71/1.90 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).
% 1.71/1.90 0 [] -class_OrderedGroup_Oab__semigroup__mult(T_a)|c_times(V_a,V_b,T_a)=c_times(V_b,V_a,T_a).
% 1.71/1.90 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).
% 1.71/1.90 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Oab__semigroup__mult(T).
% 1.71/1.90 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Osemigroup__mult(T).
% 1.71/1.90 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Ring__and__Field_Opordered__semiring(T).
% 1.71/1.90 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Olordered__ab__group__abs(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=4.
% 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=29): 1 [] -c_lesse_quals(c_times(c_HOL_Oabs(v_b(v_x(A)),t_b),c_HOL_Oabs(v_f(v_x(A)),t_b),t_b),c_times(A,c_times(c_HOL_Oabs(v_f(v_x(A)),t_b),c_HOL_Oabs(v_g(v_x(A)),t_b),t_b),t_b),t_b).
% 1.71/1.90 ** KEPT (pick-wt=8): 2 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_lesse_quals(c_0,c_HOL_Oabs(B,A),A).
% 1.71/1.90 ** 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).
% 1.71/1.90 ** KEPT (pick-wt=11): 4 [] -class_OrderedGroup_Oab__semigroup__mult(A)|c_times(B,C,A)=c_times(C,B,A).
% 1.71/1.90 ** 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).
% 1.71/1.90 ** KEPT (pick-wt=4): 6 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Oab__semigroup__mult(A).
% 1.71/1.90 ** KEPT (pick-wt=4): 7 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Osemigroup__mult(A).
% 1.71/1.90 ** KEPT (pick-wt=4): 8 [] -class_Ring__and__Field_Oordered__idom(A)|class_Ring__and__Field_Opordered__semiring(A).
% 1.71/1.90 ** KEPT (pick-wt=4): 9 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.71/1.90
% 1.71/1.90 ------------> process sos:
% 1.71/1.90 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.71/1.90 ** KEPT (pick-wt=13): 11 [] c_lesse_quals(c_HOL_Oabs(v_b(A),t_b),c_times(v_c,c_HOL_Oabs(v_g(A),t_b),t_b),t_b).
% 1.71/1.90 ** KEPT (pick-wt=2): 12 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.71/1.90 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.71/1.90
% 1.71/1.90 ======= end of input processing =======
% 1.71/1.91
% 1.71/1.91 =========== start of search ===========
% 1.71/1.91
% 1.71/1.91 -------- PROOF --------
% 1.71/1.91
% 1.71/1.91 ----> UNIT CONFLICT at 0.00 sec ----> 85 [binary,84.1,44.1] $F.
% 1.71/1.91
% 1.71/1.91 Length of proof is 11. Level of proof is 4.
% 1.71/1.91
% 1.71/1.91 ---------------- PROOF ----------------
% 1.71/1.91 % SZS status Unsatisfiable
% 1.71/1.91 % SZS output start Refutation
% See solution above
% 1.71/1.91 ------------ end of proof -------------
% 1.71/1.91
% 1.71/1.91
% 1.71/1.91 Search stopped by max_proofs option.
% 1.71/1.91
% 1.71/1.91
% 1.71/1.91 Search stopped by max_proofs option.
% 1.71/1.91
% 1.71/1.91 ============ end of search ============
% 1.71/1.91
% 1.71/1.91 -------------- statistics -------------
% 1.71/1.91 clauses given 21
% 1.71/1.91 clauses generated 211
% 1.71/1.91 clauses kept 83
% 1.71/1.91 clauses forward subsumed 169
% 1.71/1.91 clauses back subsumed 4
% 1.71/1.91 Kbytes malloced 1953
% 1.71/1.91
% 1.71/1.91 ----------- times (seconds) -----------
% 1.71/1.91 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.91 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.71/1.91
% 1.71/1.91 That finishes the proof of the theorem.
% 1.71/1.91
% 1.71/1.91 Process 16986 finished Wed Jul 27 10:01:55 2022
% 1.71/1.91 Otter interrupted
% 1.71/1.91 PROOF FOUND
%------------------------------------------------------------------------------