TSTP Solution File: ANA043-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA043-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 12:46:48 EDT 2022
% Result : Unsatisfiable 1.66s 1.82s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 11 unt; 0 nHn; 11 RR)
% Number of literals : 25 ( 2 equ; 10 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 : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 22 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_lesse_quals(c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_HOL_Oabs(v_f(v_k(v_x(A),v_xa(A))),t_b),t_b),c_times(A,c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_HOL_Oabs(v_h(v_k(v_x(A),v_xa(A))),t_b),t_b),t_b),t_b),
file('ANA043-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| c_lesse_quals(c_0,c_HOL_Oabs(B,A),A) ),
file('ANA043-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(A)
| c_times(B,c_times(C,D,A),A) = c_times(C,c_times(B,D,A),A) ),
file('ANA043-2.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('ANA043-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Oab__semigroup__mult(A) ),
file('ANA043-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Ring__and__Field_Opordered__semiring(A) ),
file('ANA043-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Olordered__ab__group__abs(A) ),
file('ANA043-2.p',unknown),
[] ).
cnf(9,axiom,
c_lesse_quals(c_HOL_Oabs(v_f(A),t_b),c_times(v_c,c_HOL_Oabs(v_h(A),t_b),t_b),t_b),
file('ANA043-2.p',unknown),
[] ).
cnf(10,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA043-2.p',unknown),
[] ).
cnf(11,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(hyper,[status(thm)],[10,7]),
[iquote('hyper,10,7')] ).
cnf(12,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(hyper,[status(thm)],[10,6]),
[iquote('hyper,10,6')] ).
cnf(13,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(hyper,[status(thm)],[10,5]),
[iquote('hyper,10,5')] ).
cnf(14,plain,
c_lesse_quals(c_0,c_HOL_Oabs(A,t_b),t_b),
inference(hyper,[status(thm)],[11,2]),
[iquote('hyper,11,2')] ).
cnf(15,plain,
c_times(A,c_times(B,C,t_b),t_b) = c_times(B,c_times(A,C,t_b),t_b),
inference(hyper,[status(thm)],[13,3]),
[iquote('hyper,13,3')] ).
cnf(17,plain,
c_lesse_quals(c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(v_f(B),t_b),t_b),c_times(c_HOL_Oabs(A,t_b),c_times(v_c,c_HOL_Oabs(v_h(B),t_b),t_b),t_b),t_b),
inference(hyper,[status(thm)],[14,4,12,9]),
[iquote('hyper,14,4,12,9')] ).
cnf(22,plain,
~ c_lesse_quals(c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_HOL_Oabs(v_f(v_k(v_x(A),v_xa(A))),t_b),t_b),c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_times(A,c_HOL_Oabs(v_h(v_k(v_x(A),v_xa(A))),t_b),t_b),t_b),t_b),
inference(para_from,[status(thm),theory(equality)],[15,1]),
[iquote('para_from,15.1.1,1.1.2')] ).
cnf(23,plain,
$false,
inference(binary,[status(thm)],[22,17]),
[iquote('binary,22.1,17.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ANA043-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:04:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.66/1.82 ----- Otter 3.3f, August 2004 -----
% 1.66/1.82 The process was started by sandbox on n012.cluster.edu,
% 1.66/1.82 Wed Jul 27 10:04:20 2022
% 1.66/1.82 The command was "./otter". The process ID is 28565.
% 1.66/1.82
% 1.66/1.82 set(prolog_style_variables).
% 1.66/1.82 set(auto).
% 1.66/1.82 dependent: set(auto1).
% 1.66/1.82 dependent: set(process_input).
% 1.66/1.82 dependent: clear(print_kept).
% 1.66/1.82 dependent: clear(print_new_demod).
% 1.66/1.82 dependent: clear(print_back_demod).
% 1.66/1.82 dependent: clear(print_back_sub).
% 1.66/1.82 dependent: set(control_memory).
% 1.66/1.82 dependent: assign(max_mem, 12000).
% 1.66/1.82 dependent: assign(pick_given_ratio, 4).
% 1.66/1.82 dependent: assign(stats_level, 1).
% 1.66/1.82 dependent: assign(max_seconds, 10800).
% 1.66/1.82 clear(print_given).
% 1.66/1.82
% 1.66/1.82 list(usable).
% 1.66/1.82 0 [] A=A.
% 1.66/1.82 0 [] c_lesse_quals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b).
% 1.66/1.82 0 [] -c_lesse_quals(c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_f(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),c_times(V_U,c_times(c_HOL_Oabs(v_l(v_x(V_U),v_xa(V_U)),t_b),c_HOL_Oabs(v_h(v_k(v_x(V_U),v_xa(V_U))),t_b),t_b),t_b),t_b).
% 1.66/1.82 0 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.66/1.82 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_lesse_quals(c_0,c_HOL_Oabs(V_a,T_a),T_a).
% 1.66/1.82 0 [] -class_OrderedGroup_Oab__semigroup__mult(T_a)|c_times(V_a,c_times(V_b,V_c,T_a),T_a)=c_times(V_b,c_times(V_a,V_c,T_a),T_a).
% 1.66/1.82 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).
% 1.66/1.82 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Oab__semigroup__mult(T).
% 1.66/1.82 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Ring__and__Field_Opordered__semiring(T).
% 1.66/1.82 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Olordered__ab__group__abs(T).
% 1.66/1.82 end_of_list.
% 1.66/1.82
% 1.66/1.82 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.66/1.82
% 1.66/1.82 This is a Horn set with equality. The strategy will be
% 1.66/1.82 Knuth-Bendix and hyper_res, with positive clauses in
% 1.66/1.82 sos and nonpositive clauses in usable.
% 1.66/1.82
% 1.66/1.82 dependent: set(knuth_bendix).
% 1.66/1.82 dependent: set(anl_eq).
% 1.66/1.82 dependent: set(para_from).
% 1.66/1.82 dependent: set(para_into).
% 1.66/1.82 dependent: clear(para_from_right).
% 1.66/1.82 dependent: clear(para_into_right).
% 1.66/1.82 dependent: set(para_from_vars).
% 1.66/1.82 dependent: set(eq_units_both_ways).
% 1.66/1.82 dependent: set(dynamic_demod_all).
% 1.66/1.82 dependent: set(dynamic_demod).
% 1.66/1.82 dependent: set(order_eq).
% 1.66/1.82 dependent: set(back_demod).
% 1.66/1.82 dependent: set(lrpo).
% 1.66/1.82 dependent: set(hyper_res).
% 1.66/1.82 dependent: clear(order_hyper).
% 1.66/1.82
% 1.66/1.82 ------------> process usable:
% 1.66/1.82 ** KEPT (pick-wt=39): 1 [] -c_lesse_quals(c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_HOL_Oabs(v_f(v_k(v_x(A),v_xa(A))),t_b),t_b),c_times(A,c_times(c_HOL_Oabs(v_l(v_x(A),v_xa(A)),t_b),c_HOL_Oabs(v_h(v_k(v_x(A),v_xa(A))),t_b),t_b),t_b),t_b).
% 1.66/1.82 ** KEPT (pick-wt=8): 2 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_lesse_quals(c_0,c_HOL_Oabs(B,A),A).
% 1.66/1.82 ** KEPT (pick-wt=17): 3 [] -class_OrderedGroup_Oab__semigroup__mult(A)|c_times(B,c_times(C,D,A),A)=c_times(C,c_times(B,D,A),A).
% 1.66/1.82 ** 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).
% 1.66/1.82 ** KEPT (pick-wt=4): 5 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Oab__semigroup__mult(A).
% 1.66/1.82 ** KEPT (pick-wt=4): 6 [] -class_Ring__and__Field_Oordered__idom(A)|class_Ring__and__Field_Opordered__semiring(A).
% 1.66/1.82 ** KEPT (pick-wt=4): 7 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.66/1.82
% 1.66/1.82 ------------> process sos:
% 1.66/1.82 ** KEPT (pick-wt=3): 8 [] A=A.
% 1.66/1.82 ** KEPT (pick-wt=13): 9 [] c_lesse_quals(c_HOL_Oabs(v_f(A),t_b),c_times(v_c,c_HOL_Oabs(v_h(A),t_b),t_b),t_b).
% 1.66/1.82 ** KEPT (pick-wt=2): 10 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.66/1.82 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 1.66/1.82
% 1.66/1.82 ======= end of input processing =======
% 1.66/1.82
% 1.66/1.82 =========== start of search ===========
% 1.66/1.82
% 1.66/1.82 -------- PROOF --------
% 1.66/1.82
% 1.66/1.82 ----> UNIT CONFLICT at 0.00 sec ----> 23 [binary,22.1,17.1] $F.
% 1.66/1.82
% 1.66/1.82 Length of proof is 7. Level of proof is 3.
% 1.66/1.82
% 1.66/1.82 ---------------- PROOF ----------------
% 1.66/1.82 % SZS status Unsatisfiable
% 1.66/1.82 % SZS output start Refutation
% See solution above
% 1.66/1.82 ------------ end of proof -------------
% 1.66/1.82
% 1.66/1.82
% 1.66/1.82 Search stopped by max_proofs option.
% 1.66/1.82
% 1.66/1.82
% 1.66/1.82 Search stopped by max_proofs option.
% 1.66/1.82
% 1.66/1.82 ============ end of search ============
% 1.66/1.82
% 1.66/1.82 -------------- statistics -------------
% 1.66/1.82 clauses given 8
% 1.66/1.82 clauses generated 19
% 1.66/1.82 clauses kept 22
% 1.66/1.82 clauses forward subsumed 11
% 1.66/1.82 clauses back subsumed 0
% 1.66/1.82 Kbytes malloced 976
% 1.66/1.82
% 1.66/1.82 ----------- times (seconds) -----------
% 1.66/1.82 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.82 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.82 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.66/1.82
% 1.66/1.82 That finishes the proof of the theorem.
% 1.66/1.82
% 1.66/1.82 Process 28565 finished Wed Jul 27 10:04:22 2022
% 1.66/1.82 Otter interrupted
% 1.66/1.82 PROOF FOUND
%------------------------------------------------------------------------------