%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA027-2 : 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 12:46:45 EDT 2022
% Result : Unsatisfiable 1.97s 2.14s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of clauses : 24 ( 14 unt; 0 nHn; 22 RR)
% Number of literals : 39 ( 2 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_lesse_quals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('ANA027-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(A)
| c_plus(c_0,B,A) = B ),
file('ANA027-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(A)
| ~ c_lesse_quals(B,c_minus(C,D,A),A)
| c_lesse_quals(c_plus(B,D,A),C,A) ),
file('ANA027-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(A)
| ~ c_lesse_quals(c_plus(B,C,A),D,A)
| c_lesse_quals(B,c_minus(D,C,A),A) ),
file('ANA027-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_Orderings_Oorder(A)
| ~ c_lesse_quals(B,C,A)
| ~ c_lesse_quals(D,B,A)
| c_lesse_quals(D,C,A) ),
file('ANA027-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_LOrder_Ojoin__semilorder(A)
| class_Orderings_Oorder(A) ),
file('ANA027-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| class_OrderedGroup_Opordered__ab__group__add(A) ),
file('ANA027-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| class_LOrder_Ojoin__semilorder(A) ),
file('ANA027-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Ocomm__monoid__add(A) ),
file('ANA027-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Olordered__ab__group__abs(A) ),
file('ANA027-2.p',unknown),
[] ).
cnf(12,axiom,
c_lesse_quals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('ANA027-2.p',unknown),
[] ).
cnf(13,axiom,
c_lesse_quals(v_g(v_x),v_k(v_x),t_b),
file('ANA027-2.p',unknown),
[] ).
cnf(14,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA027-2.p',unknown),
[] ).
cnf(15,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(hyper,[status(thm)],[14,10]),
[iquote('hyper,14,10')] ).
cnf(16,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(hyper,[status(thm)],[14,9]),
[iquote('hyper,14,9')] ).
cnf(17,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(hyper,[status(thm)],[15,8]),
[iquote('hyper,15,8')] ).
cnf(18,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(hyper,[status(thm)],[15,7]),
[iquote('hyper,15,7')] ).
cnf(20,plain,
c_plus(c_0,A,t_b) = A,
inference(hyper,[status(thm)],[16,2]),
[iquote('hyper,16,2')] ).
cnf(21,plain,
class_Orderings_Oorder(t_b),
inference(hyper,[status(thm)],[17,6]),
[iquote('hyper,17,6')] ).
cnf(22,plain,
c_lesse_quals(v_k(v_x),v_f(v_x),t_b),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[18,3,12]),20]),
[iquote('hyper,18,3,12,demod,20')] ).
cnf(23,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ c_lesse_quals(A,B,t_b)
| c_lesse_quals(c_0,c_minus(B,A,t_b),t_b) ),
inference(para_from,[status(thm),theory(equality)],[20,4]),
[iquote('para_from,19.1.1,4.2.1')] ).
cnf(25,plain,
c_lesse_quals(v_g(v_x),v_f(v_x),t_b),
inference(hyper,[status(thm)],[22,5,21,13]),
[iquote('hyper,22,5,21,13')] ).
cnf(26,plain,
c_lesse_quals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(hyper,[status(thm)],[23,18,25]),
[iquote('hyper,23,18,25')] ).
cnf(27,plain,
$false,
inference(binary,[status(thm)],[26,1]),
[iquote('binary,26.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA027-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n020.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 10:07:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.97/2.14 ----- Otter 3.3f, August 2004 -----
% 1.97/2.14 The process was started by sandbox on n020.cluster.edu,
% 1.97/2.14 Wed Jul 27 10:07:08 2022
% 1.97/2.14 The command was "./otter". The process ID is 13824.
% 1.97/2.14
% 1.97/2.14 set(prolog_style_variables).
% 1.97/2.14 set(auto).
% 1.97/2.14 dependent: set(auto1).
% 1.97/2.14 dependent: set(process_input).
% 1.97/2.14 dependent: clear(print_kept).
% 1.97/2.14 dependent: clear(print_new_demod).
% 1.97/2.14 dependent: clear(print_back_demod).
% 1.97/2.14 dependent: clear(print_back_sub).
% 1.97/2.14 dependent: set(control_memory).
% 1.97/2.14 dependent: assign(max_mem, 12000).
% 1.97/2.14 dependent: assign(pick_given_ratio, 4).
% 1.97/2.14 dependent: assign(stats_level, 1).
% 1.97/2.14 dependent: assign(max_seconds, 10800).
% 1.97/2.14 clear(print_given).
% 1.97/2.14
% 1.97/2.14 list(usable).
% 1.97/2.14 0 [] A=A.
% 1.97/2.14 0 [] c_lesse_quals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b).
% 1.97/2.14 0 [] c_lesse_quals(v_g(v_x),v_k(v_x),t_b).
% 1.97/2.14 0 [] -c_lesse_quals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b).
% 1.97/2.14 0 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.97/2.14 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_plus(c_0,V_y,T_a)=V_y.
% 1.97/2.14 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)| -c_lesse_quals(V_a,c_minus(V_c,V_b,T_a),T_a)|c_lesse_quals(c_plus(V_a,V_b,T_a),V_c,T_a).
% 1.97/2.14 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)| -c_lesse_quals(c_plus(V_a,V_b,T_a),V_c,T_a)|c_lesse_quals(V_a,c_minus(V_c,V_b,T_a),T_a).
% 1.97/2.14 0 [] -class_Orderings_Oorder(T_a)| -c_lesse_quals(V_y,V_z,T_a)| -c_lesse_quals(V_x,V_y,T_a)|c_lesse_quals(V_x,V_z,T_a).
% 1.97/2.14 0 [] -class_LOrder_Ojoin__semilorder(T)|class_Orderings_Oorder(T).
% 1.97/2.14 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T)|class_OrderedGroup_Opordered__ab__group__add(T).
% 1.97/2.14 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T)|class_LOrder_Ojoin__semilorder(T).
% 1.97/2.14 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Ocomm__monoid__add(T).
% 1.97/2.14 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Olordered__ab__group__abs(T).
% 1.97/2.14 end_of_list.
% 1.97/2.14
% 1.97/2.14 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.97/2.14
% 1.97/2.14 This is a Horn set with equality. The strategy will be
% 1.97/2.14 Knuth-Bendix and hyper_res, with positive clauses in
% 1.97/2.14 sos and nonpositive clauses in usable.
% 1.97/2.14
% 1.97/2.14 dependent: set(knuth_bendix).
% 1.97/2.14 dependent: set(anl_eq).
% 1.97/2.14 dependent: set(para_from).
% 1.97/2.14 dependent: set(para_into).
% 1.97/2.14 dependent: clear(para_from_right).
% 1.97/2.14 dependent: clear(para_into_right).
% 1.97/2.14 dependent: set(para_from_vars).
% 1.97/2.14 dependent: set(eq_units_both_ways).
% 1.97/2.14 dependent: set(dynamic_demod_all).
% 1.97/2.14 dependent: set(dynamic_demod).
% 1.97/2.14 dependent: set(order_eq).
% 1.97/2.14 dependent: set(back_demod).
% 1.97/2.14 dependent: set(lrpo).
% 1.97/2.14 dependent: set(hyper_res).
% 1.97/2.14 dependent: clear(order_hyper).
% 1.97/2.14
% 1.97/2.14 ------------> process usable:
% 1.97/2.14 ** KEPT (pick-wt=9): 1 [] -c_lesse_quals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b).
% 1.97/2.14 ** KEPT (pick-wt=8): 2 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_plus(c_0,B,A)=B.
% 1.97/2.14 ** KEPT (pick-wt=16): 3 [] -class_OrderedGroup_Opordered__ab__group__add(A)| -c_lesse_quals(B,c_minus(C,D,A),A)|c_lesse_quals(c_plus(B,D,A),C,A).
% 1.97/2.14 ** KEPT (pick-wt=16): 4 [] -class_OrderedGroup_Opordered__ab__group__add(A)| -c_lesse_quals(c_plus(B,C,A),D,A)|c_lesse_quals(B,c_minus(D,C,A),A).
% 1.97/2.14 ** KEPT (pick-wt=14): 5 [] -class_Orderings_Oorder(A)| -c_lesse_quals(B,C,A)| -c_lesse_quals(D,B,A)|c_lesse_quals(D,C,A).
% 1.97/2.14 ** KEPT (pick-wt=4): 6 [] -class_LOrder_Ojoin__semilorder(A)|class_Orderings_Oorder(A).
% 1.97/2.14 ** KEPT (pick-wt=4): 7 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|class_OrderedGroup_Opordered__ab__group__add(A).
% 1.97/2.14 ** KEPT (pick-wt=4): 8 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|class_LOrder_Ojoin__semilorder(A).
% 1.97/2.14 ** KEPT (pick-wt=4): 9 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Ocomm__monoid__add(A).
% 1.97/2.14 ** KEPT (pick-wt=4): 10 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.97/2.14
% 1.97/2.14 ------------> process sos:
% 1.97/2.14 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.97/2.14 ** KEPT (pick-wt=9): 12 [] c_lesse_quals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b).
% 1.97/2.14 ** KEPT (pick-wt=6): 13 [] c_lesse_quals(v_g(v_x),v_k(v_x),t_b).
% 1.97/2.14 ** KEPT (pick-wt=2): 14 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.97/2.14 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.97/2.14
% 1.97/2.14 ======= end of input processing =======
% 1.97/2.14
% 1.97/2.14 =========== start of search ===========
% 1.97/2.14
% 1.97/2.14 -------- PROOF --------
% 1.97/2.14
% 1.97/2.14 ----> UNIT CONFLICT at 0.00 sec ----> 27 [binary,26.1,1.1] $F.
% 1.97/2.14
% 1.97/2.14 Length of proof is 10. Level of proof is 5.
% 1.97/2.14
% 1.97/2.14 ---------------- PROOF ----------------
% 1.97/2.14 % SZS status Unsatisfiable
% 1.97/2.14 % SZS output start Refutation
% See solution above
% 1.97/2.14 ------------ end of proof -------------
% 1.97/2.14
% 1.97/2.14
% 1.97/2.14 Search stopped by max_proofs option.
% 1.97/2.14
% 1.97/2.14
% 1.97/2.14 Search stopped by max_proofs option.
% 1.97/2.14
% 1.97/2.14 ============ end of search ============
% 1.97/2.14
% 1.97/2.14 -------------- statistics -------------
% 1.97/2.14 clauses given 13
% 1.97/2.14 clauses generated 15
% 1.97/2.14 clauses kept 25
% 1.97/2.14 clauses forward subsumed 5
% 1.97/2.14 clauses back subsumed 0
% 1.97/2.14 Kbytes malloced 976
% 1.97/2.14
% 1.97/2.14 ----------- times (seconds) -----------
% 1.97/2.14 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.97/2.14
% 1.97/2.14 That finishes the proof of the theorem.
% 1.97/2.14
% 1.97/2.14 Process 13824 finished Wed Jul 27 10:07:10 2022
% 1.97/2.14 Otter interrupted
% 1.97/2.14 PROOF FOUND
%------------------------------------------------------------------------------