TSTP Solution File: ANA030-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA030-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 1.74s 1.95s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of clauses : 35 ( 22 unt; 0 nHn; 15 RR)
% Number of literals : 51 ( 15 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 55 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_lesse_quals(v_f(v_x(A)),c_plus(v_g(v_x(A)),c_times(A,c_HOL_Oabs(v_h(v_x(A)),t_b),t_b),t_b),t_b),
file('ANA030-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| ~ c_lesse_quals(c_0,B,A)
| c_HOL_Oabs(B,A) = B ),
file('ANA030-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_OrderedGroup_Oab__group__add(A)
| c_plus(B,c_uminus(C,A),A) = c_minus(B,C,A) ),
file('ANA030-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(A)
| ~ c_lesse_quals(c_minus(B,C,A),D,A)
| c_lesse_quals(B,c_plus(D,C,A),A) ),
file('ANA030-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_OrderedGroup_Oab__group__add(A)
| c_minus(B,c_uminus(C,A),A) = c_plus(B,C,A) ),
file('ANA030-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_OrderedGroup_Oab__group__add(A)
| c_uminus(c_plus(B,C,A),A) = c_plus(c_uminus(B,A),c_uminus(C,A),A) ),
file('ANA030-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_OrderedGroup_Oab__group__add(A)
| c_uminus(c_minus(B,C,A),A) = c_minus(C,B,A) ),
file('ANA030-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_OrderedGroup_Oab__group__add(A)
| c_uminus(c_uminus(B,A),A) = B ),
file('ANA030-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Orderings_Olinorder(A)
| c_lesse_quals(B,c_Orderings_Omax(C,B,A),A) ),
file('ANA030-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ class_Orderings_Olinorder(A)
| ~ c_lesse_quals(c_Orderings_Omax(B,C,A),D,A)
| c_lesse_quals(B,D,A) ),
file('ANA030-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| class_OrderedGroup_Opordered__ab__group__add(A) ),
file('ANA030-2.p',unknown),
[] ).
cnf(12,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Orderings_Olinorder(A) ),
file('ANA030-2.p',unknown),
[] ).
cnf(13,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Oab__group__add(A) ),
file('ANA030-2.p',unknown),
[] ).
cnf(14,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Olordered__ab__group__abs(A) ),
file('ANA030-2.p',unknown),
[] ).
cnf(16,axiom,
c_lesse_quals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(A),v_g(A),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(A),t_b),t_b),t_b),
file('ANA030-2.p',unknown),
[] ).
cnf(17,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA030-2.p',unknown),
[] ).
cnf(18,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(hyper,[status(thm)],[17,14]),
[iquote('hyper,17,14')] ).
cnf(19,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(hyper,[status(thm)],[17,13]),
[iquote('hyper,17,13')] ).
cnf(20,plain,
class_Orderings_Olinorder(t_b),
inference(hyper,[status(thm)],[17,12]),
[iquote('hyper,17,12')] ).
cnf(21,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(hyper,[status(thm)],[18,11]),
[iquote('hyper,18,11')] ).
cnf(22,plain,
c_uminus(c_uminus(A,t_b),t_b) = A,
inference(hyper,[status(thm)],[19,8]),
[iquote('hyper,19,8')] ).
cnf(25,plain,
c_uminus(c_minus(A,B,t_b),t_b) = c_minus(B,A,t_b),
inference(hyper,[status(thm)],[19,7]),
[iquote('hyper,19,7')] ).
cnf(26,plain,
c_uminus(c_plus(A,B,t_b),t_b) = c_plus(c_uminus(A,t_b),c_uminus(B,t_b),t_b),
inference(hyper,[status(thm)],[19,6]),
[iquote('hyper,19,6')] ).
cnf(28,plain,
c_minus(A,c_uminus(B,t_b),t_b) = c_plus(A,B,t_b),
inference(hyper,[status(thm)],[19,5]),
[iquote('hyper,19,5')] ).
cnf(30,plain,
c_plus(A,c_uminus(B,t_b),t_b) = c_minus(A,B,t_b),
inference(hyper,[status(thm)],[19,3]),
[iquote('hyper,19,3')] ).
cnf(32,plain,
c_uminus(c_plus(A,B,t_b),t_b) = c_minus(c_uminus(A,t_b),B,t_b),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),30]),
[iquote('back_demod,26,demod,30')] ).
cnf(34,plain,
c_lesse_quals(A,c_Orderings_Omax(B,A,t_b),t_b),
inference(hyper,[status(thm)],[20,9]),
[iquote('hyper,20,9')] ).
cnf(41,plain,
c_HOL_Oabs(c_Orderings_Omax(A,c_0,t_b),t_b) = c_Orderings_Omax(A,c_0,t_b),
inference(hyper,[status(thm)],[34,2,18]),
[iquote('hyper,34,2,18')] ).
cnf(43,plain,
c_lesse_quals(c_Orderings_Omax(c_minus(v_f(A),v_g(A),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(A),t_b),t_b),t_b),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),41]),
[iquote('back_demod,16,demod,41')] ).
cnf(64,plain,
c_minus(A,c_uminus(B,t_b),t_b) = c_plus(B,A,t_b),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[32,22]),25]),
[iquote('para_from,32.1.1,22.1.1.1,demod,25')] ).
cnf(73,plain,
c_plus(A,B,t_b) = c_plus(B,A,t_b),
inference(para_into,[status(thm),theory(equality)],[64,28]),
[iquote('para_into,64.1.1,28.1.1')] ).
cnf(77,plain,
~ c_lesse_quals(v_f(v_x(A)),c_plus(c_times(A,c_HOL_Oabs(v_h(v_x(A)),t_b),t_b),v_g(v_x(A)),t_b),t_b),
inference(para_from,[status(thm),theory(equality)],[73,1]),
[iquote('para_from,73.1.1,1.1.2')] ).
cnf(132,plain,
c_lesse_quals(c_minus(v_f(A),v_g(A),t_b),c_times(v_c,c_HOL_Oabs(v_h(A),t_b),t_b),t_b),
inference(hyper,[status(thm)],[43,10,20]),
[iquote('hyper,43,10,20')] ).
cnf(185,plain,
c_lesse_quals(v_f(A),c_plus(c_times(v_c,c_HOL_Oabs(v_h(A),t_b),t_b),v_g(A),t_b),t_b),
inference(hyper,[status(thm)],[132,4,21]),
[iquote('hyper,132,4,21')] ).
cnf(186,plain,
$false,
inference(binary,[status(thm)],[185,77]),
[iquote('binary,185.1,77.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA030-2 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n009.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 10:00:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.74/1.94 ----- Otter 3.3f, August 2004 -----
% 1.74/1.94 The process was started by sandbox2 on n009.cluster.edu,
% 1.74/1.94 Wed Jul 27 10:00:06 2022
% 1.74/1.94 The command was "./otter". The process ID is 10771.
% 1.74/1.94
% 1.74/1.94 set(prolog_style_variables).
% 1.74/1.94 set(auto).
% 1.74/1.94 dependent: set(auto1).
% 1.74/1.94 dependent: set(process_input).
% 1.74/1.94 dependent: clear(print_kept).
% 1.74/1.94 dependent: clear(print_new_demod).
% 1.74/1.94 dependent: clear(print_back_demod).
% 1.74/1.94 dependent: clear(print_back_sub).
% 1.74/1.94 dependent: set(control_memory).
% 1.74/1.94 dependent: assign(max_mem, 12000).
% 1.74/1.94 dependent: assign(pick_given_ratio, 4).
% 1.74/1.94 dependent: assign(stats_level, 1).
% 1.74/1.94 dependent: assign(max_seconds, 10800).
% 1.74/1.94 clear(print_given).
% 1.74/1.94
% 1.74/1.94 list(usable).
% 1.74/1.94 0 [] A=A.
% 1.74/1.94 0 [] c_lesse_quals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(V_U),v_g(V_U),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(V_U),t_b),t_b),t_b).
% 1.74/1.94 0 [] -c_lesse_quals(v_f(v_x(V_U)),c_plus(v_g(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_h(v_x(V_U)),t_b),t_b),t_b),t_b).
% 1.74/1.94 0 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.74/1.94 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)| -c_lesse_quals(c_0,V_y,T_a)|c_HOL_Oabs(V_y,T_a)=V_y.
% 1.74/1.94 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_plus(V_a,c_uminus(V_b,T_a),T_a)=c_minus(V_a,V_b,T_a).
% 1.74/1.94 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)| -c_lesse_quals(c_minus(V_a,V_b,T_a),V_c,T_a)|c_lesse_quals(V_a,c_plus(V_c,V_b,T_a),T_a).
% 1.74/1.94 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_minus(V_a,c_uminus(V_b,T_a),T_a)=c_plus(V_a,V_b,T_a).
% 1.74/1.94 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_uminus(c_plus(V_a,V_b,T_a),T_a)=c_plus(c_uminus(V_a,T_a),c_uminus(V_b,T_a),T_a).
% 1.74/1.94 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_uminus(c_minus(V_a,V_b,T_a),T_a)=c_minus(V_b,V_a,T_a).
% 1.74/1.94 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_uminus(c_uminus(V_y,T_a),T_a)=V_y.
% 1.74/1.94 0 [] -class_Orderings_Olinorder(T_b)|c_lesse_quals(V_y,c_Orderings_Omax(V_x,V_y,T_b),T_b).
% 1.74/1.94 0 [] -class_Orderings_Olinorder(T_b)| -c_lesse_quals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)|c_lesse_quals(V_x,V_z,T_b).
% 1.74/1.94 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T)|class_OrderedGroup_Opordered__ab__group__add(T).
% 1.74/1.94 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Orderings_Olinorder(T).
% 1.74/1.94 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Oab__group__add(T).
% 1.74/1.94 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Olordered__ab__group__abs(T).
% 1.74/1.94 end_of_list.
% 1.74/1.94
% 1.74/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.74/1.94
% 1.74/1.94 This is a Horn set with equality. The strategy will be
% 1.74/1.94 Knuth-Bendix and hyper_res, with positive clauses in
% 1.74/1.94 sos and nonpositive clauses in usable.
% 1.74/1.94
% 1.74/1.94 dependent: set(knuth_bendix).
% 1.74/1.94 dependent: set(anl_eq).
% 1.74/1.94 dependent: set(para_from).
% 1.74/1.94 dependent: set(para_into).
% 1.74/1.94 dependent: clear(para_from_right).
% 1.74/1.94 dependent: clear(para_into_right).
% 1.74/1.94 dependent: set(para_from_vars).
% 1.74/1.94 dependent: set(eq_units_both_ways).
% 1.74/1.94 dependent: set(dynamic_demod_all).
% 1.74/1.94 dependent: set(dynamic_demod).
% 1.74/1.94 dependent: set(order_eq).
% 1.74/1.94 dependent: set(back_demod).
% 1.74/1.94 dependent: set(lrpo).
% 1.74/1.94 dependent: set(hyper_res).
% 1.74/1.94 dependent: clear(order_hyper).
% 1.74/1.94
% 1.74/1.94 ------------> process usable:
% 1.74/1.94 ** KEPT (pick-wt=18): 1 [] -c_lesse_quals(v_f(v_x(A)),c_plus(v_g(v_x(A)),c_times(A,c_HOL_Oabs(v_h(v_x(A)),t_b),t_b),t_b),t_b).
% 1.74/1.94 ** KEPT (pick-wt=11): 2 [] -class_OrderedGroup_Olordered__ab__group__abs(A)| -c_lesse_quals(c_0,B,A)|c_HOL_Oabs(B,A)=B.
% 1.74/1.94 ** KEPT (pick-wt=13): 3 [] -class_OrderedGroup_Oab__group__add(A)|c_plus(B,c_uminus(C,A),A)=c_minus(B,C,A).
% 1.74/1.94 ** KEPT (pick-wt=16): 4 [] -class_OrderedGroup_Opordered__ab__group__add(A)| -c_lesse_quals(c_minus(B,C,A),D,A)|c_lesse_quals(B,c_plus(D,C,A),A).
% 1.74/1.94 ** KEPT (pick-wt=13): 5 [] -class_OrderedGroup_Oab__group__add(A)|c_minus(B,c_uminus(C,A),A)=c_plus(B,C,A).
% 1.74/1.94 ** KEPT (pick-wt=17): 6 [] -class_OrderedGroup_Oab__group__add(A)|c_uminus(c_plus(B,C,A),A)=c_plus(c_uminus(B,A),c_uminus(C,A),A).
% 1.74/1.94 ** KEPT (pick-wt=13): 7 [] -class_OrderedGroup_Oab__group__add(A)|c_uminus(c_minus(B,C,A),A)=c_minus(C,B,A).
% 1.74/1.94 ** KEPT (pick-wt=9): 8 [] -class_OrderedGroup_Oab__group__add(A)|c_uminus(c_uminus(B,A),A)=B.
% 1.74/1.94 ** KEPT (pick-wt=9): 9 [] -class_Orderings_Olinorder(A)|c_lesse_quals(B,c_Orderings_Omax(C,B,A),A).
% 1.74/1.95 ** KEPT (pick-wt=13): 10 [] -class_Orderings_Olinorder(A)| -c_lesse_quals(c_Orderings_Omax(B,C,A),D,A)|c_lesse_quals(B,D,A).
% 1.74/1.95 ** KEPT (pick-wt=4): 11 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|class_OrderedGroup_Opordered__ab__group__add(A).
% 1.74/1.95 ** KEPT (pick-wt=4): 12 [] -class_Ring__and__Field_Oordered__idom(A)|class_Orderings_Olinorder(A).
% 1.74/1.95 ** KEPT (pick-wt=4): 13 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Oab__group__add(A).
% 1.74/1.95 ** KEPT (pick-wt=4): 14 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.74/1.95
% 1.74/1.95 ------------> process sos:
% 1.74/1.95 ** KEPT (pick-wt=3): 15 [] A=A.
% 1.74/1.95 ** KEPT (pick-wt=20): 16 [] c_lesse_quals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(A),v_g(A),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(A),t_b),t_b),t_b).
% 1.74/1.95 ** KEPT (pick-wt=2): 17 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.74/1.95 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 1.74/1.95
% 1.74/1.95 ======= end of input processing =======
% 1.74/1.95
% 1.74/1.95 =========== start of search ===========
% 1.74/1.95
% 1.74/1.95 -------- PROOF --------
% 1.74/1.95
% 1.74/1.95 ----> UNIT CONFLICT at 0.01 sec ----> 186 [binary,185.1,77.1] $F.
% 1.74/1.95
% 1.74/1.95 Length of proof is 18. Level of proof is 6.
% 1.74/1.95
% 1.74/1.95 ---------------- PROOF ----------------
% 1.74/1.95 % SZS status Unsatisfiable
% 1.74/1.95 % SZS output start Refutation
% See solution above
% 1.74/1.95 ------------ end of proof -------------
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Search stopped by max_proofs option.
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Search stopped by max_proofs option.
% 1.74/1.95
% 1.74/1.95 ============ end of search ============
% 1.74/1.95
% 1.74/1.95 -------------- statistics -------------
% 1.74/1.95 clauses given 40
% 1.74/1.95 clauses generated 459
% 1.74/1.95 clauses kept 165
% 1.74/1.95 clauses forward subsumed 353
% 1.74/1.95 clauses back subsumed 5
% 1.74/1.95 Kbytes malloced 3906
% 1.74/1.95
% 1.74/1.95 ----------- times (seconds) -----------
% 1.74/1.95 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.74/1.95 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.74/1.95 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.95
% 1.74/1.95 That finishes the proof of the theorem.
% 1.74/1.95
% 1.74/1.95 Process 10771 finished Wed Jul 27 10:00:07 2022
% 1.74/1.95 Otter interrupted
% 1.74/1.95 PROOF FOUND
%------------------------------------------------------------------------------