%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA018-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 12:46:44 EDT 2022
% Result : Unsatisfiable 2.00s 2.19s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of clauses : 23 ( 15 unt; 0 nHn; 17 RR)
% Number of literals : 36 ( 2 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_lesse_quals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),
file('ANA018-2.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('ANA018-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Orderings_Oorder(A)
| ~ c_lesse_quals(B,C,A)
| ~ c_lesse_quals(D,B,A)
| c_lesse_quals(D,C,A) ),
file('ANA018-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_Orderings_Oorder(A)
| ~ c_less(B,C,A)
| c_lesse_quals(B,C,A) ),
file('ANA018-2.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('ANA018-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_LOrder_Ojoin__semilorder(A)
| class_Orderings_Oorder(A) ),
file('ANA018-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Osemigroup__mult(A) ),
file('ANA018-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_LOrder_Ojoin__semilorder(A) ),
file('ANA018-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Ring__and__Field_Opordered__semiring(A) ),
file('ANA018-2.p',unknown),
[] ).
cnf(11,axiom,
c_lesse_quals(c_HOL_Oabs(v_f(A),t_b),c_times(v_c,c_HOL_Oabs(v_g(A),t_b),t_b),t_b),
file('ANA018-2.p',unknown),
[] ).
cnf(12,axiom,
c_less(c_0,v_ca,t_b),
file('ANA018-2.p',unknown),
[] ).
cnf(13,axiom,
c_lesse_quals(c_HOL_Oabs(v_x(A),t_b),c_times(v_ca,c_HOL_Oabs(v_f(A),t_b),t_b),t_b),
file('ANA018-2.p',unknown),
[] ).
cnf(14,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA018-2.p',unknown),
[] ).
cnf(15,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(hyper,[status(thm)],[14,9]),
[iquote('hyper,14,9')] ).
cnf(16,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(hyper,[status(thm)],[14,8]),
[iquote('hyper,14,8')] ).
cnf(17,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(hyper,[status(thm)],[14,7]),
[iquote('hyper,14,7')] ).
cnf(18,plain,
class_Orderings_Oorder(t_b),
inference(hyper,[status(thm)],[16,6]),
[iquote('hyper,16,6')] ).
cnf(20,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)],[17,2]),
[iquote('hyper,17,2')] ).
cnf(21,plain,
~ c_lesse_quals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b),t_b),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),20]),
[iquote('back_demod,1,demod,20')] ).
cnf(22,plain,
c_lesse_quals(c_0,v_ca,t_b),
inference(hyper,[status(thm)],[12,4,18]),
[iquote('hyper,12,4,18')] ).
cnf(24,plain,
c_lesse_quals(c_times(v_ca,c_HOL_Oabs(v_f(A),t_b),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(A),t_b),t_b),t_b),t_b),
inference(hyper,[status(thm)],[22,5,15,11]),
[iquote('hyper,22,5,15,11')] ).
cnf(30,plain,
c_lesse_quals(c_HOL_Oabs(v_x(A),t_b),c_times(v_ca,c_times(v_c,c_HOL_Oabs(v_g(A),t_b),t_b),t_b),t_b),
inference(hyper,[status(thm)],[24,3,18,13]),
[iquote('hyper,24,3,18,13')] ).
cnf(31,plain,
$false,
inference(binary,[status(thm)],[30,21]),
[iquote('binary,30.1,21.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ANA018-2 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n011.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 09:56:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.00/2.19 ----- Otter 3.3f, August 2004 -----
% 2.00/2.19 The process was started by sandbox on n011.cluster.edu,
% 2.00/2.19 Wed Jul 27 09:56:55 2022
% 2.00/2.19 The command was "./otter". The process ID is 30973.
% 2.00/2.19
% 2.00/2.19 set(prolog_style_variables).
% 2.00/2.19 set(auto).
% 2.00/2.19 dependent: set(auto1).
% 2.00/2.19 dependent: set(process_input).
% 2.00/2.19 dependent: clear(print_kept).
% 2.00/2.19 dependent: clear(print_new_demod).
% 2.00/2.19 dependent: clear(print_back_demod).
% 2.00/2.19 dependent: clear(print_back_sub).
% 2.00/2.19 dependent: set(control_memory).
% 2.00/2.19 dependent: assign(max_mem, 12000).
% 2.00/2.19 dependent: assign(pick_given_ratio, 4).
% 2.00/2.19 dependent: assign(stats_level, 1).
% 2.00/2.19 dependent: assign(max_seconds, 10800).
% 2.00/2.19 clear(print_given).
% 2.00/2.19
% 2.00/2.19 list(usable).
% 2.00/2.19 0 [] A=A.
% 2.00/2.19 0 [] c_lesse_quals(c_HOL_Oabs(v_f(V_U),t_b),c_times(v_c,c_HOL_Oabs(v_g(V_U),t_b),t_b),t_b).
% 2.00/2.19 0 [] c_less(c_0,v_ca,t_b).
% 2.00/2.19 0 [] c_lesse_quals(c_HOL_Oabs(v_x(V_U),t_b),c_times(v_ca,c_HOL_Oabs(v_f(V_U),t_b),t_b),t_b).
% 2.00/2.19 0 [] -c_lesse_quals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b).
% 2.00/2.19 0 [] class_Ring__and__Field_Oordered__idom(t_b).
% 2.00/2.19 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).
% 2.00/2.19 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).
% 2.00/2.19 0 [] -class_Orderings_Oorder(T_a)| -c_less(V_x,V_y,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 2.00/2.19 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).
% 2.00/2.19 0 [] -class_LOrder_Ojoin__semilorder(T)|class_Orderings_Oorder(T).
% 2.00/2.19 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Osemigroup__mult(T).
% 2.00/2.19 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_LOrder_Ojoin__semilorder(T).
% 2.00/2.19 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Ring__and__Field_Opordered__semiring(T).
% 2.00/2.19 end_of_list.
% 2.00/2.19
% 2.00/2.19 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 2.00/2.19
% 2.00/2.19 This is a Horn set with equality. The strategy will be
% 2.00/2.19 Knuth-Bendix and hyper_res, with positive clauses in
% 2.00/2.19 sos and nonpositive clauses in usable.
% 2.00/2.19
% 2.00/2.19 dependent: set(knuth_bendix).
% 2.00/2.19 dependent: set(anl_eq).
% 2.00/2.19 dependent: set(para_from).
% 2.00/2.19 dependent: set(para_into).
% 2.00/2.19 dependent: clear(para_from_right).
% 2.00/2.19 dependent: clear(para_into_right).
% 2.00/2.19 dependent: set(para_from_vars).
% 2.00/2.19 dependent: set(eq_units_both_ways).
% 2.00/2.19 dependent: set(dynamic_demod_all).
% 2.00/2.19 dependent: set(dynamic_demod).
% 2.00/2.19 dependent: set(order_eq).
% 2.00/2.19 dependent: set(back_demod).
% 2.00/2.19 dependent: set(lrpo).
% 2.00/2.19 dependent: set(hyper_res).
% 2.00/2.19 dependent: clear(order_hyper).
% 2.00/2.19
% 2.00/2.19 ------------> process usable:
% 2.00/2.19 ** KEPT (pick-wt=16): 1 [] -c_lesse_quals(c_HOL_Oabs(v_x(v_xa),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_xa),t_b),t_b),t_b).
% 2.00/2.19 ** 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).
% 2.00/2.19 ** KEPT (pick-wt=14): 3 [] -class_Orderings_Oorder(A)| -c_lesse_quals(B,C,A)| -c_lesse_quals(D,B,A)|c_lesse_quals(D,C,A).
% 2.00/2.19 ** KEPT (pick-wt=10): 4 [] -class_Orderings_Oorder(A)| -c_less(B,C,A)|c_lesse_quals(B,C,A).
% 2.00/2.19 ** 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).
% 2.00/2.19 ** KEPT (pick-wt=4): 6 [] -class_LOrder_Ojoin__semilorder(A)|class_Orderings_Oorder(A).
% 2.00/2.19 ** KEPT (pick-wt=4): 7 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Osemigroup__mult(A).
% 2.00/2.19 ** KEPT (pick-wt=4): 8 [] -class_Ring__and__Field_Oordered__idom(A)|class_LOrder_Ojoin__semilorder(A).
% 2.00/2.19 ** KEPT (pick-wt=4): 9 [] -class_Ring__and__Field_Oordered__idom(A)|class_Ring__and__Field_Opordered__semiring(A).
% 2.00/2.19
% 2.00/2.19 ------------> process sos:
% 2.00/2.19 ** KEPT (pick-wt=3): 10 [] A=A.
% 2.00/2.19 ** KEPT (pick-wt=13): 11 [] c_lesse_quals(c_HOL_Oabs(v_f(A),t_b),c_times(v_c,c_HOL_Oabs(v_g(A),t_b),t_b),t_b).
% 2.00/2.19 ** KEPT (pick-wt=4): 12 [] c_less(c_0,v_ca,t_b).
% 2.00/2.19 ** KEPT (pick-wt=13): 13 [] c_lesse_quals(c_HOL_Oabs(v_x(A),t_b),c_times(v_ca,c_HOL_Oabs(v_f(A),t_b),t_b),t_b).
% 2.00/2.19 ** KEPT (pick-wt=2): 14 [] class_Ring__and__Field_Oordered__idom(t_b).
% 2.00/2.19 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 2.00/2.19
% 2.00/2.19 ======= end of input processing =======
% 2.00/2.19
% 2.00/2.19 =========== start of search ===========
% 2.00/2.19
% 2.00/2.19 -------- PROOF --------
% 2.00/2.19
% 2.00/2.19 ----> UNIT CONFLICT at 0.00 sec ----> 31 [binary,30.1,21.1] $F.
% 2.00/2.19
% 2.00/2.19 Length of proof is 9. Level of proof is 5.
% 2.00/2.19
% 2.00/2.19 ---------------- PROOF ----------------
% 2.00/2.19 % SZS status Unsatisfiable
% 2.00/2.19 % SZS output start Refutation
% See solution above
% 2.00/2.19 ------------ end of proof -------------
% 2.00/2.19
% 2.00/2.19
% 2.00/2.19 Search stopped by max_proofs option.
% 2.00/2.19
% 2.00/2.19
% 2.00/2.19 Search stopped by max_proofs option.
% 2.00/2.19
% 2.00/2.19 ============ end of search ============
% 2.00/2.19
% 2.00/2.19 -------------- statistics -------------
% 2.00/2.19 clauses given 15
% 2.00/2.19 clauses generated 24
% 2.00/2.19 clauses kept 29
% 2.00/2.19 clauses forward subsumed 11
% 2.00/2.19 clauses back subsumed 0
% 2.00/2.19 Kbytes malloced 976
% 2.00/2.19
% 2.00/2.19 ----------- times (seconds) -----------
% 2.00/2.19 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.00/2.19
% 2.00/2.19 That finishes the proof of the theorem.
% 2.00/2.19
% 2.00/2.19 Process 30973 finished Wed Jul 27 09:56:57 2022
% 2.00/2.19 Otter interrupted
% 2.00/2.19 PROOF FOUND
%------------------------------------------------------------------------------