TSTP Solution File: SWV002-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWV002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 13:19:39 EDT 2022
% Result : Unsatisfiable 1.87s 2.06s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 12 ( 9 unt; 1 nHn; 11 RR)
% Number of literals : 18 ( 2 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( less_than(A,B)
| ~ less_than(A,C)
| ~ less_than(C,B) ),
file('SWV002-1.p',unknown),
[] ).
cnf(4,axiom,
~ less_than(A,A),
file('SWV002-1.p',unknown),
[] ).
cnf(10,axiom,
( less_than(A,i)
| ~ less_than(A,j)
| ~ less_than(a(A),a(k)) ),
file('SWV002-1.p',unknown),
[] ).
cnf(13,axiom,
~ less_than(q,i),
file('SWV002-1.p',unknown),
[] ).
cnf(14,axiom,
~ less_than(j,q),
file('SWV002-1.p',unknown),
[] ).
cnf(22,axiom,
( less_than(A,B)
| less_than(B,A)
| A = B ),
file('SWV002-1.p',unknown),
[] ).
cnf(25,axiom,
less_than(a(j),a(k)),
file('SWV002-1.p',unknown),
[] ).
cnf(26,axiom,
less_than(a(q),a(j)),
file('SWV002-1.p',unknown),
[] ).
cnf(96,plain,
less_than(a(q),a(k)),
inference(hyper,[status(thm)],[26,3,25]),
[iquote('hyper,26,3,25')] ).
cnf(410,plain,
q = j,
inference(flip,[status(thm),theory(equality)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[96,10,22]),13,14])]),
[iquote('hyper,96,10,22,unit_del,13,14,flip.1')] ).
cnf(425,plain,
less_than(a(j),a(j)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),410]),
[iquote('back_demod,26,demod,410')] ).
cnf(426,plain,
$false,
inference(binary,[status(thm)],[425,4]),
[iquote('binary,425.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 05:34:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.81/2.03 ----- Otter 3.3f, August 2004 -----
% 1.81/2.03 The process was started by sandbox2 on n006.cluster.edu,
% 1.81/2.03 Wed Jul 27 05:34:02 2022
% 1.81/2.03 The command was "./otter". The process ID is 30729.
% 1.81/2.03
% 1.81/2.03 set(prolog_style_variables).
% 1.81/2.03 set(auto).
% 1.81/2.03 dependent: set(auto1).
% 1.81/2.03 dependent: set(process_input).
% 1.81/2.03 dependent: clear(print_kept).
% 1.81/2.03 dependent: clear(print_new_demod).
% 1.81/2.03 dependent: clear(print_back_demod).
% 1.81/2.03 dependent: clear(print_back_sub).
% 1.81/2.03 dependent: set(control_memory).
% 1.81/2.03 dependent: assign(max_mem, 12000).
% 1.81/2.03 dependent: assign(pick_given_ratio, 4).
% 1.81/2.03 dependent: assign(stats_level, 1).
% 1.81/2.03 dependent: assign(max_seconds, 10800).
% 1.81/2.03 clear(print_given).
% 1.81/2.03
% 1.81/2.03 list(usable).
% 1.81/2.03 0 [] A=A.
% 1.81/2.03 0 [] predecessor(successor(X))=X.
% 1.81/2.03 0 [] successor(predecessor(X))=X.
% 1.81/2.03 0 [] X=Y|predecessor(X)!=predecessor(Y).
% 1.81/2.03 0 [] X=Y|successor(X)!=successor(Y).
% 1.81/2.03 0 [] less_than(predecessor(X),X).
% 1.81/2.03 0 [] less_than(X,successor(X)).
% 1.81/2.03 0 [] less_than(X,Z)| -less_than(X,Y)| -less_than(Y,Z).
% 1.81/2.03 0 [] less_than(X,Y)|less_than(Y,X)|X=Y.
% 1.81/2.03 0 [] -less_than(X,X).
% 1.81/2.03 0 [] -less_than(X,Y)| -less_than(Y,X).
% 1.81/2.03 0 [] less_than(Y,Z)|X!=Y| -less_than(X,Z).
% 1.81/2.03 0 [] less_than(Z,Y)|X!=Y| -less_than(Z,X).
% 1.81/2.03 0 [] -less_than(n,j).
% 1.81/2.03 0 [] less_than(k,j).
% 1.81/2.03 0 [] -less_than(k,i).
% 1.81/2.03 0 [] less_than(i,n).
% 1.81/2.03 0 [] less_than(a(j),a(k)).
% 1.81/2.03 0 [] less_than(X,i)| -less_than(X,j)| -less_than(a(X),a(k)).
% 1.81/2.03 0 [] less_than(X,i)|less_than(n,X)| -less_than(one,i)| -less_than(a(X),a(predecessor(i))).
% 1.81/2.03 0 [] -less_than(one,X)| -less_than(X,i)| -less_than(a(X),a(predecessor(X))).
% 1.81/2.03 0 [] -less_than(q,i).
% 1.81/2.03 0 [] -less_than(j,q).
% 1.81/2.03 0 [] less_than(a(q),a(j)).
% 1.81/2.03 end_of_list.
% 1.81/2.03
% 1.81/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.81/2.03
% 1.81/2.03 This ia a non-Horn set with equality. The strategy will be
% 1.81/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.81/2.03 deletion, with positive clauses in sos and nonpositive
% 1.81/2.03 clauses in usable.
% 1.81/2.03
% 1.81/2.03 dependent: set(knuth_bendix).
% 1.81/2.03 dependent: set(anl_eq).
% 1.81/2.03 dependent: set(para_from).
% 1.81/2.03 dependent: set(para_into).
% 1.81/2.03 dependent: clear(para_from_right).
% 1.81/2.03 dependent: clear(para_into_right).
% 1.81/2.03 dependent: set(para_from_vars).
% 1.81/2.03 dependent: set(eq_units_both_ways).
% 1.81/2.03 dependent: set(dynamic_demod_all).
% 1.81/2.03 dependent: set(dynamic_demod).
% 1.81/2.03 dependent: set(order_eq).
% 1.81/2.03 dependent: set(back_demod).
% 1.81/2.03 dependent: set(lrpo).
% 1.81/2.03 dependent: set(hyper_res).
% 1.81/2.03 dependent: set(unit_deletion).
% 1.81/2.03 dependent: set(factor).
% 1.81/2.03
% 1.81/2.03 ------------> process usable:
% 1.81/2.03 ** KEPT (pick-wt=8): 1 [] A=B|predecessor(A)!=predecessor(B).
% 1.81/2.03 ** KEPT (pick-wt=8): 2 [] A=B|successor(A)!=successor(B).
% 1.81/2.03 ** KEPT (pick-wt=9): 3 [] less_than(A,B)| -less_than(A,C)| -less_than(C,B).
% 1.81/2.03 ** KEPT (pick-wt=3): 4 [] -less_than(A,A).
% 1.81/2.03 ** KEPT (pick-wt=6): 5 [] -less_than(A,B)| -less_than(B,A).
% 1.81/2.03 ** KEPT (pick-wt=9): 6 [] less_than(A,B)|C!=A| -less_than(C,B).
% 1.81/2.03 ** KEPT (pick-wt=9): 7 [] less_than(A,B)|C!=B| -less_than(A,C).
% 1.81/2.03 ** KEPT (pick-wt=3): 8 [] -less_than(n,j).
% 1.81/2.03 ** KEPT (pick-wt=3): 9 [] -less_than(k,i).
% 1.81/2.03 ** KEPT (pick-wt=11): 10 [] less_than(A,i)| -less_than(A,j)| -less_than(a(A),a(k)).
% 1.81/2.03 ** KEPT (pick-wt=15): 11 [] less_than(A,i)|less_than(n,A)| -less_than(one,i)| -less_than(a(A),a(predecessor(i))).
% 1.81/2.03 ** KEPT (pick-wt=12): 12 [] -less_than(one,A)| -less_than(A,i)| -less_than(a(A),a(predecessor(A))).
% 1.81/2.03 ** KEPT (pick-wt=3): 13 [] -less_than(q,i).
% 1.81/2.03 ** KEPT (pick-wt=3): 14 [] -less_than(j,q).
% 1.81/2.03
% 1.81/2.03 ------------> process sos:
% 1.81/2.03 ** KEPT (pick-wt=3): 15 [] A=A.
% 1.81/2.03 ** KEPT (pick-wt=5): 16 [] predecessor(successor(A))=A.
% 1.81/2.03 ---> New Demodulator: 17 [new_demod,16] predecessor(successor(A))=A.
% 1.81/2.03 ** KEPT (pick-wt=5): 18 [] successor(predecessor(A))=A.
% 1.81/2.03 ---> New Demodulator: 19 [new_demod,18] successor(predecessor(A))=A.
% 1.81/2.03 ** KEPT (pick-wt=4): 20 [] less_than(predecessor(A),A).
% 1.81/2.03 ** KEPT (pick-wt=4): 21 [] less_than(A,successor(A)).
% 1.81/2.03 ** KEPT (pick-wt=9): 22 [] less_than(A,B)|less_than(B,A)|A=B.
% 1.81/2.03 ** KEPT (pick-wt=3): 23 [] less_than(k,j).
% 1.81/2.03 ** KEPT (pick-wt=3): 24 [] less_than(i,n).
% 1.81/2.03 ** KEPT (pick-wt=5): 25 [] less_than(a(j),a(k)).
% 1.81/2.03 ** KEPT (pick-wt=5): 26 [] less_than(a(q),a(j)).
% 1.81/2.03 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 1.81/2.03 >>>> Starting back demodulation with 17.
% 1.81/2.03 >>>> Starting back demodulation with 19.
% 1.81/2.03
% 1.81/2.03 ======= end of input processing =======
% 1.87/2.06
% 1.87/2.06 =========== start of search ===========
% 1.87/2.06
% 1.87/2.06 -------- PROOF --------
% 1.87/2.06
% 1.87/2.06 ----> UNIT CONFLICT at 0.02 sec ----> 426 [binary,425.1,4.1] $F.
% 1.87/2.06
% 1.87/2.06 Length of proof is 3. Level of proof is 3.
% 1.87/2.06
% 1.87/2.06 ---------------- PROOF ----------------
% 1.87/2.06 % SZS status Unsatisfiable
% 1.87/2.06 % SZS output start Refutation
% See solution above
% 1.87/2.06 ------------ end of proof -------------
% 1.87/2.06
% 1.87/2.06
% 1.87/2.06 Search stopped by max_proofs option.
% 1.87/2.06
% 1.87/2.06
% 1.87/2.06 Search stopped by max_proofs option.
% 1.87/2.06
% 1.87/2.06 ============ end of search ============
% 1.87/2.06
% 1.87/2.06 -------------- statistics -------------
% 1.87/2.06 clauses given 25
% 1.87/2.06 clauses generated 801
% 1.87/2.06 clauses kept 422
% 1.87/2.06 clauses forward subsumed 429
% 1.87/2.06 clauses back subsumed 2
% 1.87/2.06 Kbytes malloced 1953
% 1.87/2.06
% 1.87/2.06 ----------- times (seconds) -----------
% 1.87/2.06 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.87/2.06 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.06 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.87/2.06
% 1.87/2.06 That finishes the proof of the theorem.
% 1.87/2.06
% 1.87/2.06 Process 30729 finished Wed Jul 27 05:34:03 2022
% 1.87/2.06 Otter interrupted
% 1.87/2.06 PROOF FOUND
%------------------------------------------------------------------------------