%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA039-2 : 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 12:46:47 EDT 2022
% Result : Unsatisfiable 1.97s 2.16s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 18 ( 11 unt; 0 nHn; 11 RR)
% Number of literals : 29 ( 0 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 21 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_lesse_quals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file('ANA039-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| c_lesse_quals(B,c_HOL_Oabs(B,A),A) ),
file('ANA039-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| c_lesse_quals(c_0,c_HOL_Oabs(B,A),A) ),
file('ANA039-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Orderings_Oorder(A)
| ~ c_lesse_quals(B,C,A)
| ~ c_lesse_quals(D,B,A)
| c_lesse_quals(D,C,A) ),
file('ANA039-2.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(B,D,A),c_times(C,D,A),A) ),
file('ANA039-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Ring__and__Field_Opordered__semiring(A) ),
file('ANA039-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Orderings_Oorder(A) ),
file('ANA039-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Olordered__ab__group__abs(A) ),
file('ANA039-2.p',unknown),
[] ).
cnf(9,axiom,
c_lesse_quals(c_HOL_Oabs(v_h(A),t_a),c_times(v_c,c_HOL_Oabs(v_f(A),t_a),t_a),t_a),
file('ANA039-2.p',unknown),
[] ).
cnf(10,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file('ANA039-2.p',unknown),
[] ).
cnf(11,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(hyper,[status(thm)],[10,8]),
[iquote('hyper,10,8')] ).
cnf(12,plain,
class_Orderings_Oorder(t_a),
inference(hyper,[status(thm)],[10,7]),
[iquote('hyper,10,7')] ).
cnf(13,plain,
class_Ring__and__Field_Opordered__semiring(t_a),
inference(hyper,[status(thm)],[10,6]),
[iquote('hyper,10,6')] ).
cnf(14,plain,
c_lesse_quals(c_0,c_HOL_Oabs(A,t_a),t_a),
inference(hyper,[status(thm)],[11,3]),
[iquote('hyper,11,3')] ).
cnf(15,plain,
c_lesse_quals(A,c_HOL_Oabs(A,t_a),t_a),
inference(hyper,[status(thm)],[11,2]),
[iquote('hyper,11,2')] ).
cnf(20,plain,
c_lesse_quals(c_times(A,c_HOL_Oabs(B,t_a),t_a),c_times(c_HOL_Oabs(A,t_a),c_HOL_Oabs(B,t_a),t_a),t_a),
inference(hyper,[status(thm)],[15,5,13,14]),
[iquote('hyper,15,5,13,14')] ).
cnf(134,plain,
c_lesse_quals(c_HOL_Oabs(v_h(A),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(A),t_a),t_a),t_a),
inference(hyper,[status(thm)],[20,4,12,9]),
[iquote('hyper,20,4,12,9')] ).
cnf(135,plain,
$false,
inference(binary,[status(thm)],[134,1]),
[iquote('binary,134.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ANA039-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % 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 10:15:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.97/2.16 ----- Otter 3.3f, August 2004 -----
% 1.97/2.16 The process was started by sandbox on n026.cluster.edu,
% 1.97/2.16 Wed Jul 27 10:15:39 2022
% 1.97/2.16 The command was "./otter". The process ID is 16981.
% 1.97/2.16
% 1.97/2.16 set(prolog_style_variables).
% 1.97/2.16 set(auto).
% 1.97/2.16 dependent: set(auto1).
% 1.97/2.16 dependent: set(process_input).
% 1.97/2.16 dependent: clear(print_kept).
% 1.97/2.16 dependent: clear(print_new_demod).
% 1.97/2.16 dependent: clear(print_back_demod).
% 1.97/2.16 dependent: clear(print_back_sub).
% 1.97/2.16 dependent: set(control_memory).
% 1.97/2.16 dependent: assign(max_mem, 12000).
% 1.97/2.16 dependent: assign(pick_given_ratio, 4).
% 1.97/2.16 dependent: assign(stats_level, 1).
% 1.97/2.16 dependent: assign(max_seconds, 10800).
% 1.97/2.16 clear(print_given).
% 1.97/2.16
% 1.97/2.16 list(usable).
% 1.97/2.16 0 [] c_lesse_quals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a).
% 1.97/2.16 0 [] -c_lesse_quals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a).
% 1.97/2.16 0 [] class_Ring__and__Field_Oordered__idom(t_a).
% 1.97/2.16 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_lesse_quals(V_a,c_HOL_Oabs(V_a,T_a),T_a).
% 1.97/2.16 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_lesse_quals(c_0,c_HOL_Oabs(V_a,T_a),T_a).
% 1.97/2.16 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).
% 1.97/2.16 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_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a).
% 1.97/2.16 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Ring__and__Field_Opordered__semiring(T).
% 1.97/2.16 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Orderings_Oorder(T).
% 1.97/2.16 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Olordered__ab__group__abs(T).
% 1.97/2.16 end_of_list.
% 1.97/2.16
% 1.97/2.16 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.97/2.16
% 1.97/2.16 This is a Horn set without equality. The strategy will
% 1.97/2.16 be hyperresolution, with satellites in sos and nuclei
% 1.97/2.16 in usable.
% 1.97/2.16
% 1.97/2.16 dependent: set(hyper_res).
% 1.97/2.16 dependent: clear(order_hyper).
% 1.97/2.16
% 1.97/2.16 ------------> process usable:
% 1.97/2.16 ** KEPT (pick-wt=15): 1 [] -c_lesse_quals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a).
% 1.97/2.16 ** KEPT (pick-wt=8): 2 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_lesse_quals(B,c_HOL_Oabs(B,A),A).
% 1.97/2.16 ** KEPT (pick-wt=8): 3 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_lesse_quals(c_0,c_HOL_Oabs(B,A),A).
% 1.97/2.16 ** KEPT (pick-wt=14): 4 [] -class_Orderings_Oorder(A)| -c_lesse_quals(B,C,A)| -c_lesse_quals(D,B,A)|c_lesse_quals(D,C,A).
% 1.97/2.16 ** 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(B,D,A),c_times(C,D,A),A).
% 1.97/2.16 ** KEPT (pick-wt=4): 6 [] -class_Ring__and__Field_Oordered__idom(A)|class_Ring__and__Field_Opordered__semiring(A).
% 1.97/2.16 ** KEPT (pick-wt=4): 7 [] -class_Ring__and__Field_Oordered__idom(A)|class_Orderings_Oorder(A).
% 1.97/2.16 ** KEPT (pick-wt=4): 8 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.97/2.16
% 1.97/2.16 ------------> process sos:
% 1.97/2.16 ** KEPT (pick-wt=13): 9 [] c_lesse_quals(c_HOL_Oabs(v_h(A),t_a),c_times(v_c,c_HOL_Oabs(v_f(A),t_a),t_a),t_a).
% 1.97/2.16 ** KEPT (pick-wt=2): 10 [] class_Ring__and__Field_Oordered__idom(t_a).
% 1.97/2.16
% 1.97/2.16 ======= end of input processing =======
% 1.97/2.16
% 1.97/2.16 =========== start of search ===========
% 1.97/2.16
% 1.97/2.16 -------- PROOF --------
% 1.97/2.16
% 1.97/2.16 ----> UNIT CONFLICT at 0.00 sec ----> 135 [binary,134.1,1.1] $F.
% 1.97/2.16
% 1.97/2.16 Length of proof is 7. Level of proof is 4.
% 1.97/2.16
% 1.97/2.16 ---------------- PROOF ----------------
% 1.97/2.16 % SZS status Unsatisfiable
% 1.97/2.16 % SZS output start Refutation
% See solution above
% 1.97/2.16 ------------ end of proof -------------
% 1.97/2.16
% 1.97/2.16
% 1.97/2.16 Search stopped by max_proofs option.
% 1.97/2.16
% 1.97/2.16
% 1.97/2.16 Search stopped by max_proofs option.
% 1.97/2.16
% 1.97/2.16 ============ end of search ============
% 1.97/2.16
% 1.97/2.16 -------------- statistics -------------
% 1.97/2.16 clauses given 19
% 1.97/2.16 clauses generated 210
% 1.97/2.16 clauses kept 134
% 1.97/2.16 clauses forward subsumed 86
% 1.97/2.16 clauses back subsumed 42
% 1.97/2.16 Kbytes malloced 976
% 1.97/2.16
% 1.97/2.16 ----------- times (seconds) -----------
% 1.97/2.16 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.97/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.16 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.97/2.16
% 1.97/2.16 That finishes the proof of the theorem.
% 1.97/2.16
% 1.97/2.16 Process 16981 finished Wed Jul 27 10:15:41 2022
% 1.97/2.16 Otter interrupted
% 1.97/2.16 PROOF FOUND
%------------------------------------------------------------------------------