%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWV006-1 : 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 1.94s 2.12s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 8 RR)
% Number of literals : 13 ( 0 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( less_than(A,B)
| ~ less_than(A,C)
| ~ less_than(C,B) ),
file('SWV006-1.p',unknown),
[] ).
cnf(4,axiom,
~ less_than(A,A),
file('SWV006-1.p',unknown),
[] ).
cnf(10,axiom,
( less_than(A,i)
| ~ less_than(A,successor(n))
| ~ less_than(a(A),a(m)) ),
file('SWV006-1.p',unknown),
[] ).
cnf(19,axiom,
less_than(A,successor(A)),
file('SWV006-1.p',unknown),
[] ).
cnf(22,axiom,
less_than(i,n),
file('SWV006-1.p',unknown),
[] ).
cnf(23,axiom,
less_than(a(i),a(m)),
file('SWV006-1.p',unknown),
[] ).
cnf(37,plain,
less_than(i,successor(n)),
inference(hyper,[status(thm)],[19,3,22]),
[iquote('hyper,19,3,22')] ).
cnf(82,plain,
less_than(i,i),
inference(hyper,[status(thm)],[23,10,37]),
[iquote('hyper,23,10,37')] ).
cnf(83,plain,
$false,
inference(binary,[status(thm)],[82,4]),
[iquote('binary,82.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % 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 05:40:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.94/2.12 ----- Otter 3.3f, August 2004 -----
% 1.94/2.12 The process was started by sandbox2 on n006.cluster.edu,
% 1.94/2.12 Wed Jul 27 05:40:47 2022
% 1.94/2.12 The command was "./otter". The process ID is 2097.
% 1.94/2.12
% 1.94/2.12 set(prolog_style_variables).
% 1.94/2.12 set(auto).
% 1.94/2.12 dependent: set(auto1).
% 1.94/2.12 dependent: set(process_input).
% 1.94/2.12 dependent: clear(print_kept).
% 1.94/2.12 dependent: clear(print_new_demod).
% 1.94/2.12 dependent: clear(print_back_demod).
% 1.94/2.12 dependent: clear(print_back_sub).
% 1.94/2.12 dependent: set(control_memory).
% 1.94/2.12 dependent: assign(max_mem, 12000).
% 1.94/2.12 dependent: assign(pick_given_ratio, 4).
% 1.94/2.12 dependent: assign(stats_level, 1).
% 1.94/2.12 dependent: assign(max_seconds, 10800).
% 1.94/2.12 clear(print_given).
% 1.94/2.12
% 1.94/2.12 list(usable).
% 1.94/2.12 0 [] A=A.
% 1.94/2.12 0 [] predecessor(successor(X))=X.
% 1.94/2.12 0 [] successor(predecessor(X))=X.
% 1.94/2.12 0 [] X=Y|predecessor(X)!=predecessor(Y).
% 1.94/2.12 0 [] X=Y|successor(X)!=successor(Y).
% 1.94/2.12 0 [] less_than(predecessor(X),X).
% 1.94/2.12 0 [] less_than(X,successor(X)).
% 1.94/2.12 0 [] less_than(X,Z)| -less_than(X,Y)| -less_than(Y,Z).
% 1.94/2.12 0 [] less_than(X,Y)|less_than(Y,X)|X=Y.
% 1.94/2.12 0 [] -less_than(X,X).
% 1.94/2.12 0 [] -less_than(X,Y)| -less_than(Y,X).
% 1.94/2.12 0 [] less_than(Y,Z)|X!=Y| -less_than(X,Z).
% 1.94/2.12 0 [] less_than(Z,Y)|X!=Y| -less_than(Z,X).
% 1.94/2.12 0 [] -less_than(n,m).
% 1.94/2.12 0 [] less_than(i,m).
% 1.94/2.12 0 [] less_than(i,n).
% 1.94/2.12 0 [] -less_than(i,one).
% 1.94/2.12 0 [] less_than(a(i),a(m)).
% 1.94/2.12 0 [] less_than(X,i)| -less_than(X,successor(n))| -less_than(a(X),a(m)).
% 1.94/2.12 0 [] less_than(X,i)|less_than(n,X)| -less_than(one,i)| -less_than(a(X),a(predecessor(i))).
% 1.94/2.12 0 [] -less_than(one,X)| -less_than(X,i)| -less_than(a(X),a(predecessor(X))).
% 1.94/2.12 end_of_list.
% 1.94/2.12
% 1.94/2.12 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.94/2.12
% 1.94/2.12 This ia a non-Horn set with equality. The strategy will be
% 1.94/2.12 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.94/2.12 deletion, with positive clauses in sos and nonpositive
% 1.94/2.12 clauses in usable.
% 1.94/2.12
% 1.94/2.12 dependent: set(knuth_bendix).
% 1.94/2.12 dependent: set(anl_eq).
% 1.94/2.12 dependent: set(para_from).
% 1.94/2.12 dependent: set(para_into).
% 1.94/2.12 dependent: clear(para_from_right).
% 1.94/2.12 dependent: clear(para_into_right).
% 1.94/2.12 dependent: set(para_from_vars).
% 1.94/2.12 dependent: set(eq_units_both_ways).
% 1.94/2.12 dependent: set(dynamic_demod_all).
% 1.94/2.12 dependent: set(dynamic_demod).
% 1.94/2.12 dependent: set(order_eq).
% 1.94/2.12 dependent: set(back_demod).
% 1.94/2.12 dependent: set(lrpo).
% 1.94/2.12 dependent: set(hyper_res).
% 1.94/2.12 dependent: set(unit_deletion).
% 1.94/2.12 dependent: set(factor).
% 1.94/2.12
% 1.94/2.12 ------------> process usable:
% 1.94/2.12 ** KEPT (pick-wt=8): 1 [] A=B|predecessor(A)!=predecessor(B).
% 1.94/2.12 ** KEPT (pick-wt=8): 2 [] A=B|successor(A)!=successor(B).
% 1.94/2.12 ** KEPT (pick-wt=9): 3 [] less_than(A,B)| -less_than(A,C)| -less_than(C,B).
% 1.94/2.12 ** KEPT (pick-wt=3): 4 [] -less_than(A,A).
% 1.94/2.12 ** KEPT (pick-wt=6): 5 [] -less_than(A,B)| -less_than(B,A).
% 1.94/2.12 ** KEPT (pick-wt=9): 6 [] less_than(A,B)|C!=A| -less_than(C,B).
% 1.94/2.12 ** KEPT (pick-wt=9): 7 [] less_than(A,B)|C!=B| -less_than(A,C).
% 1.94/2.12 ** KEPT (pick-wt=3): 8 [] -less_than(n,m).
% 1.94/2.12 ** KEPT (pick-wt=3): 9 [] -less_than(i,one).
% 1.94/2.12 ** KEPT (pick-wt=12): 10 [] less_than(A,i)| -less_than(A,successor(n))| -less_than(a(A),a(m)).
% 1.94/2.12 ** KEPT (pick-wt=15): 11 [] less_than(A,i)|less_than(n,A)| -less_than(one,i)| -less_than(a(A),a(predecessor(i))).
% 1.94/2.12 ** KEPT (pick-wt=12): 12 [] -less_than(one,A)| -less_than(A,i)| -less_than(a(A),a(predecessor(A))).
% 1.94/2.12
% 1.94/2.12 ------------> process sos:
% 1.94/2.12 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.94/2.12 ** KEPT (pick-wt=5): 14 [] predecessor(successor(A))=A.
% 1.94/2.12 ---> New Demodulator: 15 [new_demod,14] predecessor(successor(A))=A.
% 1.94/2.12 ** KEPT (pick-wt=5): 16 [] successor(predecessor(A))=A.
% 1.94/2.12 ---> New Demodulator: 17 [new_demod,16] successor(predecessor(A))=A.
% 1.94/2.12 ** KEPT (pick-wt=4): 18 [] less_than(predecessor(A),A).
% 1.94/2.12 ** KEPT (pick-wt=4): 19 [] less_than(A,successor(A)).
% 1.94/2.12 ** KEPT (pick-wt=9): 20 [] less_than(A,B)|less_than(B,A)|A=B.
% 1.94/2.12 ** KEPT (pick-wt=3): 21 [] less_than(i,m).
% 1.94/2.12 ** KEPT (pick-wt=3): 22 [] less_than(i,n).
% 1.94/2.12 ** KEPT (pick-wt=5): 23 [] less_than(a(i),a(m)).
% 1.94/2.12 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.94/2.12 >>>> Starting back demodulation with 15.
% 1.94/2.12 >>>> Starting back demodulation with 17.
% 1.94/2.12
% 1.94/2.12 ======= end of input processing =======
% 1.94/2.12
% 1.94/2.12 =========== start of search ===========
% 1.94/2.12
% 1.94/2.12 -------- PROOF --------
% 1.94/2.12
% 1.94/2.12 ----> UNIT CONFLICT at 0.00 sec ----> 83 [binary,82.1,4.1] $F.
% 1.94/2.12
% 1.94/2.12 Length of proof is 2. Level of proof is 2.
% 1.94/2.12
% 1.94/2.12 ---------------- PROOF ----------------
% 1.94/2.12 % SZS status Unsatisfiable
% 1.94/2.12 % SZS output start Refutation
% See solution above
% 1.94/2.12 ------------ end of proof -------------
% 1.94/2.12
% 1.94/2.12
% 1.94/2.12 Search stopped by max_proofs option.
% 1.94/2.12
% 1.94/2.12
% 1.94/2.12 Search stopped by max_proofs option.
% 1.94/2.12
% 1.94/2.12 ============ end of search ============
% 1.94/2.12
% 1.94/2.12 -------------- statistics -------------
% 1.94/2.12 clauses given 12
% 1.94/2.12 clauses generated 102
% 1.94/2.12 clauses kept 80
% 1.94/2.12 clauses forward subsumed 44
% 1.94/2.12 clauses back subsumed 0
% 1.94/2.12 Kbytes malloced 976
% 1.94/2.12
% 1.94/2.12 ----------- times (seconds) -----------
% 1.94/2.12 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.12 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.94/2.12
% 1.94/2.12 That finishes the proof of the theorem.
% 1.94/2.12
% 1.94/2.12 Process 2097 finished Wed Jul 27 05:40:48 2022
% 1.94/2.12 Otter interrupted
% 1.94/2.12 PROOF FOUND
%------------------------------------------------------------------------------