TSTP Solution File: SET821-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET821-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 13:14:19 EDT 2022
% Result : Unsatisfiable 1.74s 1.93s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 8 unt; 9 nHn; 10 RR)
% Number of literals : 38 ( 1 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 38 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_Orderings_Oorder(A)
| ~ c_less(B,B,A) ),
file('SET821-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(A,B,C)
| ~ c_in(A,c_uminus(B,tc_set(C)),C) ),
file('SET821-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(A,B,C)
| c_in(A,c_insert(D,B,C),C) ),
file('SET821-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(A,c_insert(B,C,D),D)
| c_in(A,C,D)
| A = B ),
file('SET821-2.p',unknown),
[] ).
cnf(5,axiom,
( c_in(v_c,A,tc_IntDef_Oint)
| ~ c_in(v_b,A,tc_IntDef_Oint)
| c_in(v_a,A,tc_IntDef_Oint) ),
file('SET821-2.p',unknown),
[] ).
cnf(8,axiom,
c_in(A,c_insert(A,B,C),C),
file('SET821-2.p',unknown),
[] ).
cnf(9,axiom,
c_less(v_a,v_b,tc_IntDef_Oint),
file('SET821-2.p',unknown),
[] ).
cnf(10,axiom,
c_less(v_b,v_c,tc_IntDef_Oint),
file('SET821-2.p',unknown),
[] ).
cnf(11,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('SET821-2.p',unknown),
[] ).
cnf(13,plain,
( c_less(A,v_b,tc_IntDef_Oint)
| ~ c_in(v_a,c_insert(A,B,C),C)
| c_in(v_a,B,C) ),
inference(para_into,[status(thm),theory(equality)],[9,4]),
[iquote('para_into,9.1.1,4.3.1')] ).
cnf(17,plain,
( c_less(v_b,A,tc_IntDef_Oint)
| ~ c_in(v_c,c_insert(A,B,C),C)
| c_in(v_c,B,C) ),
inference(para_into,[status(thm),theory(equality)],[10,4]),
[iquote('para_into,10.1.2,4.3.1')] ).
cnf(19,plain,
( c_in(v_c,c_insert(v_b,A,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_a,c_insert(v_b,A,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(hyper,[status(thm)],[8,5]),
[iquote('hyper,8,5')] ).
cnf(20,plain,
c_in(A,c_insert(B,c_insert(A,C,D),D),D),
inference(hyper,[status(thm)],[8,3]),
[iquote('hyper,8,3')] ).
cnf(38,plain,
c_in(A,c_insert(B,c_insert(C,c_insert(A,D,E),E),E),E),
inference(hyper,[status(thm)],[20,3]),
[iquote('hyper,20,3')] ).
cnf(73,plain,
( c_in(v_c,c_insert(v_b,A,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(v_b,v_b,tc_IntDef_Oint)
| c_in(v_a,A,tc_IntDef_Oint) ),
inference(hyper,[status(thm)],[19,13]),
[iquote('hyper,19,13')] ).
cnf(248,plain,
( c_in(v_c,c_insert(v_b,A,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_a,A,tc_IntDef_Oint) ),
inference(hyper,[status(thm)],[73,1,11]),
[iquote('hyper,73,1,11')] ).
cnf(249,plain,
( c_in(v_a,A,tc_IntDef_Oint)
| c_less(v_b,v_b,tc_IntDef_Oint)
| c_in(v_c,A,tc_IntDef_Oint) ),
inference(hyper,[status(thm)],[248,17]),
[iquote('hyper,248,17')] ).
cnf(296,plain,
( c_in(v_a,A,tc_IntDef_Oint)
| c_in(v_c,A,tc_IntDef_Oint) ),
inference(hyper,[status(thm)],[249,1,11]),
[iquote('hyper,249,1,11')] ).
cnf(306,plain,
c_in(v_c,c_uminus(c_insert(v_a,A,tc_IntDef_Oint),tc_set(tc_IntDef_Oint)),tc_IntDef_Oint),
inference(hyper,[status(thm)],[296,2,8]),
[iquote('hyper,296,2,8')] ).
cnf(327,plain,
$false,
inference(hyper,[status(thm)],[306,2,38]),
[iquote('hyper,306,2,38')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET821-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n017.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 10:14:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.74/1.93 ----- Otter 3.3f, August 2004 -----
% 1.74/1.93 The process was started by sandbox on n017.cluster.edu,
% 1.74/1.93 Wed Jul 27 10:14:03 2022
% 1.74/1.93 The command was "./otter". The process ID is 21470.
% 1.74/1.93
% 1.74/1.93 set(prolog_style_variables).
% 1.74/1.93 set(auto).
% 1.74/1.93 dependent: set(auto1).
% 1.74/1.93 dependent: set(process_input).
% 1.74/1.93 dependent: clear(print_kept).
% 1.74/1.93 dependent: clear(print_new_demod).
% 1.74/1.93 dependent: clear(print_back_demod).
% 1.74/1.93 dependent: clear(print_back_sub).
% 1.74/1.93 dependent: set(control_memory).
% 1.74/1.93 dependent: assign(max_mem, 12000).
% 1.74/1.93 dependent: assign(pick_given_ratio, 4).
% 1.74/1.93 dependent: assign(stats_level, 1).
% 1.74/1.93 dependent: assign(max_seconds, 10800).
% 1.74/1.93 clear(print_given).
% 1.74/1.93
% 1.74/1.93 list(usable).
% 1.74/1.93 0 [] A=A.
% 1.74/1.93 0 [] -class_Orderings_Oorder(T_a)| -c_less(V_x,V_x,T_a).
% 1.74/1.93 0 [] -c_in(V_c,V_A,T_a)| -c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a).
% 1.74/1.93 0 [] c_in(V_c,V_A,T_a)|c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a).
% 1.74/1.93 0 [] -c_in(V_a,V_B,T_a)|c_in(V_a,c_insert(V_b,V_B,T_a),T_a).
% 1.74/1.93 0 [] c_in(V_x,c_insert(V_x,V_B,T_a),T_a).
% 1.74/1.93 0 [] -c_in(V_a,c_insert(V_b,V_A,T_a),T_a)|c_in(V_a,V_A,T_a)|V_a=V_b.
% 1.74/1.93 0 [] c_less(v_a,v_b,tc_IntDef_Oint).
% 1.74/1.93 0 [] c_less(v_b,v_c,tc_IntDef_Oint).
% 1.74/1.93 0 [] c_in(v_c,V_U,tc_IntDef_Oint)| -c_in(v_b,V_U,tc_IntDef_Oint)|c_in(v_a,V_U,tc_IntDef_Oint).
% 1.74/1.93 0 [] class_Orderings_Oorder(tc_IntDef_Oint).
% 1.74/1.93 end_of_list.
% 1.74/1.93
% 1.74/1.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.74/1.93
% 1.74/1.93 This ia a non-Horn set with equality. The strategy will be
% 1.74/1.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.74/1.93 deletion, with positive clauses in sos and nonpositive
% 1.74/1.93 clauses in usable.
% 1.74/1.93
% 1.74/1.93 dependent: set(knuth_bendix).
% 1.74/1.93 dependent: set(anl_eq).
% 1.74/1.93 dependent: set(para_from).
% 1.74/1.93 dependent: set(para_into).
% 1.74/1.93 dependent: clear(para_from_right).
% 1.74/1.93 dependent: clear(para_into_right).
% 1.74/1.93 dependent: set(para_from_vars).
% 1.74/1.93 dependent: set(eq_units_both_ways).
% 1.74/1.93 dependent: set(dynamic_demod_all).
% 1.74/1.93 dependent: set(dynamic_demod).
% 1.74/1.93 dependent: set(order_eq).
% 1.74/1.93 dependent: set(back_demod).
% 1.74/1.93 dependent: set(lrpo).
% 1.74/1.93 dependent: set(hyper_res).
% 1.74/1.93 dependent: set(unit_deletion).
% 1.74/1.93 dependent: set(factor).
% 1.74/1.93
% 1.74/1.93 ------------> process usable:
% 1.74/1.93 ** KEPT (pick-wt=6): 1 [] -class_Orderings_Oorder(A)| -c_less(B,B,A).
% 1.74/1.93 ** KEPT (pick-wt=11): 2 [] -c_in(A,B,C)| -c_in(A,c_uminus(B,tc_set(C)),C).
% 1.74/1.93 ** KEPT (pick-wt=11): 3 [] -c_in(A,B,C)|c_in(A,c_insert(D,B,C),C).
% 1.74/1.93 ** KEPT (pick-wt=14): 4 [] -c_in(A,c_insert(B,C,D),D)|c_in(A,C,D)|A=B.
% 1.74/1.93 ** KEPT (pick-wt=12): 5 [] c_in(v_c,A,tc_IntDef_Oint)| -c_in(v_b,A,tc_IntDef_Oint)|c_in(v_a,A,tc_IntDef_Oint).
% 1.74/1.93
% 1.74/1.93 ------------> process sos:
% 1.74/1.93 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.74/1.93 ** KEPT (pick-wt=11): 7 [] c_in(A,B,C)|c_in(A,c_uminus(B,tc_set(C)),C).
% 1.74/1.93 ** KEPT (pick-wt=7): 8 [] c_in(A,c_insert(A,B,C),C).
% 1.74/1.93 ** KEPT (pick-wt=4): 9 [] c_less(v_a,v_b,tc_IntDef_Oint).
% 1.74/1.93 ** KEPT (pick-wt=4): 10 [] c_less(v_b,v_c,tc_IntDef_Oint).
% 1.74/1.93 ** KEPT (pick-wt=2): 11 [] class_Orderings_Oorder(tc_IntDef_Oint).
% 1.74/1.93 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.74/1.93
% 1.74/1.93 ======= end of input processing =======
% 1.74/1.93
% 1.74/1.93 =========== start of search ===========
% 1.74/1.93
% 1.74/1.93 -------- PROOF --------
% 1.74/1.93
% 1.74/1.93 -----> EMPTY CLAUSE at 0.04 sec ----> 327 [hyper,306,2,38] $F.
% 1.74/1.93
% 1.74/1.93 Length of proof is 10. Level of proof is 6.
% 1.74/1.93
% 1.74/1.93 ---------------- PROOF ----------------
% 1.74/1.93 % SZS status Unsatisfiable
% 1.74/1.93 % SZS output start Refutation
% See solution above
% 1.74/1.93 ------------ end of proof -------------
% 1.74/1.93
% 1.74/1.93
% 1.74/1.93 Search stopped by max_proofs option.
% 1.74/1.93
% 1.74/1.93
% 1.74/1.93 Search stopped by max_proofs option.
% 1.74/1.93
% 1.74/1.93 ============ end of search ============
% 1.74/1.93
% 1.74/1.93 -------------- statistics -------------
% 1.74/1.93 clauses given 29
% 1.74/1.93 clauses generated 565
% 1.74/1.93 clauses kept 326
% 1.74/1.93 clauses forward subsumed 247
% 1.74/1.93 clauses back subsumed 119
% 1.74/1.93 Kbytes malloced 1953
% 1.74/1.93
% 1.74/1.93 ----------- times (seconds) -----------
% 1.74/1.93 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.74/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.93 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.93
% 1.74/1.93 That finishes the proof of the theorem.
% 1.74/1.93
% 1.74/1.93 Process 21470 finished Wed Jul 27 10:14:04 2022
% 1.74/1.93 Otter interrupted
% 1.74/1.93 PROOF FOUND
%------------------------------------------------------------------------------