TSTP Solution File: NUM027-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM027-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:07:29 EDT 2022
% Result : Unsatisfiable 1.96s 2.11s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 8 unt; 5 nHn; 11 RR)
% Number of literals : 28 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ less(A,B)
| ~ less(C,A)
| less(C,B) ),
file('NUM027-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ e_qualish(A,B)
| e_qualish(multiply(A,C),multiply(B,C)) ),
file('NUM027-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ less(A,B)
| ~ e_qualish(A,B) ),
file('NUM027-1.p',unknown),
[] ).
cnf(10,axiom,
~ less(A,A),
file('NUM027-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ less(A,B)
| e_qualish(C,n0)
| less(multiply(A,C),multiply(B,C)) ),
file('NUM027-1.p',unknown),
[] ).
cnf(13,axiom,
~ less(b,a),
file('NUM027-1.p',unknown),
[] ).
cnf(14,axiom,
~ e_qualish(c,n0),
file('NUM027-1.p',unknown),
[] ).
cnf(20,axiom,
( less(A,B)
| e_qualish(B,A)
| less(B,A) ),
file('NUM027-1.p',unknown),
[] ).
cnf(21,axiom,
less(multiply(b,c),multiply(a,c)),
file('NUM027-1.p',unknown),
[] ).
cnf(98,plain,
( e_qualish(a,b)
| less(a,b) ),
inference(hyper,[status(thm)],[20,13]),
[iquote('hyper,20,13')] ).
cnf(110,plain,
( less(a,b)
| e_qualish(b,a) ),
inference(hyper,[status(thm)],[20,13]),
[iquote('hyper,20,13')] ).
cnf(122,plain,
( e_qualish(a,b)
| e_qualish(A,n0)
| less(multiply(a,A),multiply(b,A)) ),
inference(hyper,[status(thm)],[98,12]),
[iquote('hyper,98,12')] ).
cnf(1224,plain,
e_qualish(a,b),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[122,3,21]),14,10]),
[iquote('hyper,122,3,21,unit_del,14,10')] ).
cnf(1226,plain,
e_qualish(b,a),
inference(hyper,[status(thm)],[1224,9,110]),
[iquote('hyper,1224,9,110')] ).
cnf(1243,plain,
e_qualish(multiply(b,A),multiply(a,A)),
inference(hyper,[status(thm)],[1226,8]),
[iquote('hyper,1226,8')] ).
cnf(1322,plain,
$false,
inference(hyper,[status(thm)],[1243,9,21]),
[iquote('hyper,1243,9,21')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM027-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.14 % Command : otter-tptp-script %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Jul 27 09:49:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.96/2.11 ----- Otter 3.3f, August 2004 -----
% 1.96/2.11 The process was started by sandbox2 on n008.cluster.edu,
% 1.96/2.11 Wed Jul 27 09:49:24 2022
% 1.96/2.11 The command was "./otter". The process ID is 6809.
% 1.96/2.11
% 1.96/2.11 set(prolog_style_variables).
% 1.96/2.11 set(auto).
% 1.96/2.11 dependent: set(auto1).
% 1.96/2.11 dependent: set(process_input).
% 1.96/2.11 dependent: clear(print_kept).
% 1.96/2.11 dependent: clear(print_new_demod).
% 1.96/2.11 dependent: clear(print_back_demod).
% 1.96/2.11 dependent: clear(print_back_sub).
% 1.96/2.11 dependent: set(control_memory).
% 1.96/2.11 dependent: assign(max_mem, 12000).
% 1.96/2.11 dependent: assign(pick_given_ratio, 4).
% 1.96/2.11 dependent: assign(stats_level, 1).
% 1.96/2.11 dependent: assign(max_seconds, 10800).
% 1.96/2.11 clear(print_given).
% 1.96/2.11
% 1.96/2.11 list(usable).
% 1.96/2.11 0 [] e_qualish(add(A,n0),A).
% 1.96/2.11 0 [] e_qualish(add(A,successor(B)),successor(add(A,B))).
% 1.96/2.11 0 [] e_qualish(multiply(A,n0),n0).
% 1.96/2.11 0 [] e_qualish(multiply(A,successor(B)),add(multiply(A,B),A)).
% 1.96/2.11 0 [] -e_qualish(successor(A),successor(B))|e_qualish(A,B).
% 1.96/2.11 0 [] -e_qualish(A,B)|e_qualish(successor(A),successor(B)).
% 1.96/2.11 0 [] -less(A,B)| -less(C,A)|less(C,B).
% 1.96/2.11 0 [] -e_qualish(add(successor(A),B),C)|less(B,C).
% 1.96/2.11 0 [] -less(A,B)|e_qualish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B).
% 1.96/2.11 0 [] e_qualish(X,X).
% 1.96/2.11 0 [] -e_qualish(X,Y)|e_qualish(Y,X).
% 1.96/2.11 0 [] -e_qualish(X,Y)| -e_qualish(Y,Z)|e_qualish(X,Z).
% 1.96/2.11 0 [] -e_qualish(A,B)|e_qualish(multiply(A,C),multiply(B,C)).
% 1.96/2.11 0 [] -less(A,B)| -e_qualish(A,B).
% 1.96/2.11 0 [] less(A,B)|e_qualish(B,A)|less(B,A).
% 1.96/2.11 0 [] -less(A,A).
% 1.96/2.11 0 [] -e_qualish(successor(A),n0).
% 1.96/2.11 0 [] -less(A,B)|e_qualish(C,n0)|less(multiply(A,C),multiply(B,C)).
% 1.96/2.11 0 [] -less(b,a).
% 1.96/2.11 0 [] less(multiply(b,c),multiply(a,c)).
% 1.96/2.11 0 [] -e_qualish(c,n0).
% 1.96/2.11 end_of_list.
% 1.96/2.11
% 1.96/2.11 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.96/2.11
% 1.96/2.11 This is a non-Horn set without equality. The strategy will
% 1.96/2.11 be ordered hyper_res, unit deletion, and factoring, with
% 1.96/2.11 satellites in sos and with nuclei in usable.
% 1.96/2.11
% 1.96/2.11 dependent: set(hyper_res).
% 1.96/2.11 dependent: set(factor).
% 1.96/2.11 dependent: set(unit_deletion).
% 1.96/2.11
% 1.96/2.11 ------------> process usable:
% 1.96/2.11 ** KEPT (pick-wt=8): 1 [] -e_qualish(successor(A),successor(B))|e_qualish(A,B).
% 1.96/2.11 ** KEPT (pick-wt=8): 2 [] -e_qualish(A,B)|e_qualish(successor(A),successor(B)).
% 1.96/2.11 ** KEPT (pick-wt=9): 3 [] -less(A,B)| -less(C,A)|less(C,B).
% 1.96/2.11 ** KEPT (pick-wt=9): 4 [] -e_qualish(add(successor(A),B),C)|less(B,C).
% 1.96/2.11 ** KEPT (pick-wt=11): 5 [] -less(A,B)|e_qualish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B).
% 1.96/2.11 ** KEPT (pick-wt=6): 6 [] -e_qualish(A,B)|e_qualish(B,A).
% 1.96/2.11 ** KEPT (pick-wt=9): 7 [] -e_qualish(A,B)| -e_qualish(B,C)|e_qualish(A,C).
% 1.96/2.11 ** KEPT (pick-wt=10): 8 [] -e_qualish(A,B)|e_qualish(multiply(A,C),multiply(B,C)).
% 1.96/2.11 ** KEPT (pick-wt=6): 9 [] -less(A,B)| -e_qualish(A,B).
% 1.96/2.11 ** KEPT (pick-wt=3): 10 [] -less(A,A).
% 1.96/2.11 ** KEPT (pick-wt=4): 11 [] -e_qualish(successor(A),n0).
% 1.96/2.11 ** KEPT (pick-wt=13): 12 [] -less(A,B)|e_qualish(C,n0)|less(multiply(A,C),multiply(B,C)).
% 1.96/2.11 ** KEPT (pick-wt=3): 13 [] -less(b,a).
% 1.96/2.11 ** KEPT (pick-wt=3): 14 [] -e_qualish(c,n0).
% 1.96/2.11
% 1.96/2.11 ------------> process sos:
% 1.96/2.11 ** KEPT (pick-wt=5): 15 [] e_qualish(add(A,n0),A).
% 1.96/2.11 ** KEPT (pick-wt=9): 16 [] e_qualish(add(A,successor(B)),successor(add(A,B))).
% 1.96/2.11 ** KEPT (pick-wt=5): 17 [] e_qualish(multiply(A,n0),n0).
% 1.96/2.11 ** KEPT (pick-wt=10): 18 [] e_qualish(multiply(A,successor(B)),add(multiply(A,B),A)).
% 1.96/2.11 ** KEPT (pick-wt=3): 19 [] e_qualish(A,A).
% 1.96/2.11 ** KEPT (pick-wt=9): 20 [] less(A,B)|e_qualish(B,A)|less(B,A).
% 1.96/2.11 ** KEPT (pick-wt=7): 21 [] less(multiply(b,c),multiply(a,c)).
% 1.96/2.11
% 1.96/2.11 ======= end of input processing =======
% 1.96/2.11
% 1.96/2.11 =========== start of search ===========
% 1.96/2.11
% 1.96/2.11
% 1.96/2.11 Resetting weight limit to 9.
% 1.96/2.11
% 1.96/2.11
% 1.96/2.11 Resetting weight limit to 9.
% 1.96/2.11
% 1.96/2.11 sos_size=1092
% 1.96/2.11
% 1.96/2.11 -------- PROOF --------
% 1.96/2.11
% 1.96/2.11 -----> EMPTY CLAUSE at 0.19 sec ----> 1322 [hyper,1243,9,21] $F.
% 1.96/2.11
% 1.96/2.11 Length of proof is 6. Level of proof is 5.
% 1.96/2.11
% 1.96/2.11 ---------------- PROOF ----------------
% 1.96/2.11 % SZS status Unsatisfiable
% 1.96/2.11 % SZS output start Refutation
% See solution above
% 1.96/2.11 ------------ end of proof -------------
% 1.96/2.11
% 1.96/2.11
% 1.96/2.11 Search stopped by max_proofs option.
% 1.96/2.11
% 1.96/2.11
% 1.96/2.11 Search stopped by max_proofs option.
% 1.96/2.11
% 1.96/2.11 ============ end of search ============
% 1.96/2.11
% 1.96/2.11 -------------- statistics -------------
% 1.96/2.11 clauses given 300
% 1.96/2.11 clauses generated 20880
% 1.96/2.11 clauses kept 1321
% 1.96/2.11 clauses forward subsumed 2104
% 1.96/2.11 clauses back subsumed 34
% 1.96/2.11 Kbytes malloced 4882
% 1.96/2.11
% 1.96/2.11 ----------- times (seconds) -----------
% 1.96/2.11 user CPU time 0.19 (0 hr, 0 min, 0 sec)
% 1.96/2.11 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.96/2.11 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.96/2.11
% 1.96/2.11 That finishes the proof of the theorem.
% 1.96/2.11
% 1.96/2.11 Process 6809 finished Wed Jul 27 09:49:25 2022
% 1.96/2.12 Otter interrupted
% 1.96/2.12 PROOF FOUND
%------------------------------------------------------------------------------