TSTP Solution File: KRS010-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS010-1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:00:57 EDT 2022
% Result : Unsatisfiable 1.71s 1.92s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 32 ( 11 unt; 12 nHn; 32 RR)
% Number of literals : 71 ( 0 equ; 23 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ f(exist),
file('KRS010-1.p',unknown),
[] ).
cnf(2,axiom,
( c(A)
| d(A)
| ~ a(A) ),
file('KRS010-1.p',unknown),
[] ).
cnf(5,axiom,
( e_qualish(A,B)
| ~ e(C)
| ~ r(C,A)
| ~ r(C,B)
| ~ c(A)
| ~ c(B) ),
file('KRS010-1.p',unknown),
[] ).
cnf(6,axiom,
( r3least(A)
| ~ e(A) ),
file('KRS010-1.p',unknown),
[] ).
cnf(7,axiom,
( a(A)
| ~ e(B)
| ~ r(B,A) ),
file('KRS010-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ r3least(A)
| ~ e_qualish(u2r2(A),u2r1(A)) ),
file('KRS010-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ r3least(A)
| ~ e_qualish(u2r3(A),u2r1(A)) ),
file('KRS010-1.p',unknown),
[] ).
cnf(20,axiom,
( ~ r3least(A)
| ~ e_qualish(u2r3(A),u2r2(A)) ),
file('KRS010-1.p',unknown),
[] ).
cnf(21,axiom,
( r(A,u2r1(A))
| ~ r3least(A) ),
file('KRS010-1.p',unknown),
[] ).
cnf(22,axiom,
( r(A,u2r2(A))
| ~ r3least(A) ),
file('KRS010-1.p',unknown),
[] ).
cnf(23,axiom,
( r(A,u2r3(A))
| ~ r3least(A) ),
file('KRS010-1.p',unknown),
[] ).
cnf(30,axiom,
( f(A)
| e_qualish(B,C)
| ~ r(A,B)
| ~ r(A,C)
| ~ d(B)
| ~ d(C) ),
file('KRS010-1.p',unknown),
[] ).
cnf(34,axiom,
e(exist),
file('KRS010-1.p',unknown),
[] ).
cnf(35,plain,
r3least(exist),
inference(hyper,[status(thm)],[34,6]),
[iquote('hyper,34,6')] ).
cnf(36,plain,
r(exist,u2r3(exist)),
inference(hyper,[status(thm)],[35,23]),
[iquote('hyper,35,23')] ).
cnf(37,plain,
r(exist,u2r2(exist)),
inference(hyper,[status(thm)],[35,22]),
[iquote('hyper,35,22')] ).
cnf(38,plain,
r(exist,u2r1(exist)),
inference(hyper,[status(thm)],[35,21]),
[iquote('hyper,35,21')] ).
cnf(39,plain,
a(u2r3(exist)),
inference(hyper,[status(thm)],[36,7,34]),
[iquote('hyper,36,7,34')] ).
cnf(40,plain,
( c(u2r3(exist))
| d(u2r3(exist)) ),
inference(hyper,[status(thm)],[39,2]),
[iquote('hyper,39,2')] ).
cnf(41,plain,
a(u2r2(exist)),
inference(hyper,[status(thm)],[37,7,34]),
[iquote('hyper,37,7,34')] ).
cnf(42,plain,
a(u2r1(exist)),
inference(hyper,[status(thm)],[38,7,34]),
[iquote('hyper,38,7,34')] ).
cnf(43,plain,
( c(u2r2(exist))
| d(u2r2(exist)) ),
inference(hyper,[status(thm)],[41,2]),
[iquote('hyper,41,2')] ).
cnf(44,plain,
( c(u2r1(exist))
| d(u2r1(exist)) ),
inference(hyper,[status(thm)],[42,2]),
[iquote('hyper,42,2')] ).
cnf(47,plain,
( c(u2r2(exist))
| e_qualish(u2r3(exist),u2r2(exist))
| c(u2r3(exist)) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[43,30,36,37,40]),1]),
[iquote('hyper,43,30,36,37,40,unit_del,1')] ).
cnf(50,plain,
( c(u2r1(exist))
| e_qualish(u2r2(exist),u2r1(exist))
| c(u2r2(exist)) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[44,30,37,38,43]),1]),
[iquote('hyper,44,30,37,38,43,unit_del,1')] ).
cnf(51,plain,
( c(u2r1(exist))
| e_qualish(u2r3(exist),u2r1(exist))
| c(u2r3(exist)) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[44,30,36,38,40]),1]),
[iquote('hyper,44,30,36,38,40,unit_del,1')] ).
cnf(58,plain,
( e_qualish(u2r2(exist),u2r1(exist))
| c(u2r2(exist))
| e_qualish(u2r3(exist),u2r1(exist))
| e_qualish(u2r3(exist),u2r2(exist)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[50,5,34,36,38,47])]),
[iquote('hyper,50,5,34,36,38,47,factor_simp')] ).
cnf(62,plain,
( e_qualish(u2r3(exist),u2r1(exist))
| c(u2r3(exist))
| e_qualish(u2r2(exist),u2r1(exist))
| e_qualish(u2r3(exist),u2r2(exist)) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[51,5,34,37,38,47])]),
[iquote('hyper,51,5,34,37,38,47,factor_simp')] ).
cnf(89,plain,
( e_qualish(u2r3(exist),u2r1(exist))
| e_qualish(u2r2(exist),u2r1(exist))
| e_qualish(u2r3(exist),u2r2(exist)) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[62,5,34,36,37,58])])])])]),
[iquote('hyper,62,5,34,36,37,58,factor_simp,factor_simp,factor_simp,factor_simp')] ).
cnf(90,plain,
( e_qualish(u2r2(exist),u2r1(exist))
| e_qualish(u2r3(exist),u2r2(exist)) ),
inference(hyper,[status(thm)],[89,19,35]),
[iquote('hyper,89,19,35')] ).
cnf(93,plain,
e_qualish(u2r3(exist),u2r2(exist)),
inference(hyper,[status(thm)],[90,18,35]),
[iquote('hyper,90,18,35')] ).
cnf(95,plain,
$false,
inference(hyper,[status(thm)],[93,20,35]),
[iquote('hyper,93,20,35')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KRS010-1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 03:28:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.91 ----- Otter 3.3f, August 2004 -----
% 1.71/1.91 The process was started by sandbox on n019.cluster.edu,
% 1.71/1.91 Wed Jul 27 03:28:22 2022
% 1.71/1.91 The command was "./otter". The process ID is 2454.
% 1.71/1.91
% 1.71/1.91 set(prolog_style_variables).
% 1.71/1.91 set(auto).
% 1.71/1.91 dependent: set(auto1).
% 1.71/1.91 dependent: set(process_input).
% 1.71/1.91 dependent: clear(print_kept).
% 1.71/1.91 dependent: clear(print_new_demod).
% 1.71/1.91 dependent: clear(print_back_demod).
% 1.71/1.91 dependent: clear(print_back_sub).
% 1.71/1.91 dependent: set(control_memory).
% 1.71/1.91 dependent: assign(max_mem, 12000).
% 1.71/1.91 dependent: assign(pick_given_ratio, 4).
% 1.71/1.91 dependent: assign(stats_level, 1).
% 1.71/1.91 dependent: assign(max_seconds, 10800).
% 1.71/1.91 clear(print_given).
% 1.71/1.91
% 1.71/1.91 list(usable).
% 1.71/1.91 0 [] e(exist).
% 1.71/1.91 0 [] -f(exist).
% 1.71/1.91 0 [] c(X1)|d(X1)| -a(X1).
% 1.71/1.91 0 [] a(X1)| -d(X1).
% 1.71/1.91 0 [] a(X1)| -c(X1).
% 1.71/1.91 0 [] e_qualish(X4,X3)| -e(X1)| -r(X1,X4)| -r(X1,X3)| -c(X4)| -c(X3).
% 1.71/1.91 0 [] r3least(X1)| -e(X1).
% 1.71/1.91 0 [] a(X2)| -e(X1)| -r(X1,X2).
% 1.71/1.91 0 [] e(X1)| -a(u1r1(X1))| -r3least(X1)| -e_qualish(u1r3(X1),u1r2(X1)).
% 1.71/1.91 0 [] e(X1)|c(u1r2(X1))| -a(u1r1(X1))| -r3least(X1).
% 1.71/1.91 0 [] e(X1)|c(u1r3(X1))| -a(u1r1(X1))| -r3least(X1).
% 1.71/1.91 0 [] e(X1)|r(X1,u1r2(X1))| -a(u1r1(X1))| -r3least(X1).
% 1.71/1.91 0 [] e(X1)|r(X1,u1r3(X1))| -a(u1r1(X1))| -r3least(X1).
% 1.71/1.91 0 [] e(X1)|r(X1,u1r1(X1))| -r3least(X1)| -e_qualish(u1r3(X1),u1r2(X1)).
% 1.71/1.91 0 [] e(X1)|r(X1,u1r1(X1))|c(u1r2(X1))| -r3least(X1).
% 1.71/1.91 0 [] e(X1)|r(X1,u1r1(X1))|c(u1r3(X1))| -r3least(X1).
% 1.71/1.91 0 [] e(X1)|r(X1,u1r1(X1))|r(X1,u1r2(X1))| -r3least(X1).
% 1.71/1.91 0 [] e(X1)|r(X1,u1r1(X1))|r(X1,u1r3(X1))| -r3least(X1).
% 1.71/1.91 0 [] -r3least(X1)| -e_qualish(u2r2(X1),u2r1(X1)).
% 1.71/1.91 0 [] -r3least(X1)| -e_qualish(u2r3(X1),u2r1(X1)).
% 1.71/1.91 0 [] -r3least(X1)| -e_qualish(u2r3(X1),u2r2(X1)).
% 1.71/1.91 0 [] r(X1,u2r1(X1))| -r3least(X1).
% 1.71/1.91 0 [] r(X1,u2r2(X1))| -r3least(X1).
% 1.71/1.91 0 [] r(X1,u2r3(X1))| -r3least(X1).
% 1.71/1.91 0 [] r3least(X1)|e_qualish(X4,X3)|e_qualish(X4,X2)|e_qualish(X3,X2)| -r(X1,X4)| -r(X1,X3)| -r(X1,X2).
% 1.71/1.91 0 [] d(u3r1(X1))| -f(X1).
% 1.71/1.91 0 [] d(u3r2(X1))| -f(X1).
% 1.71/1.91 0 [] -f(X1)| -e_qualish(u3r2(X1),u3r1(X1)).
% 1.71/1.91 0 [] r(X1,u3r1(X1))| -f(X1).
% 1.71/1.91 0 [] r(X1,u3r2(X1))| -f(X1).
% 1.71/1.91 0 [] f(X1)|e_qualish(X3,X2)| -r(X1,X3)| -r(X1,X2)| -d(X3)| -d(X2).
% 1.71/1.91 end_of_list.
% 1.71/1.91
% 1.71/1.91 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=7.
% 1.71/1.91
% 1.71/1.91 This is a non-Horn set without equality. The strategy will
% 1.71/1.91 be ordered hyper_res, unit deletion, and factoring, with
% 1.71/1.91 satellites in sos and with nuclei in usable.
% 1.71/1.91
% 1.71/1.91 dependent: set(hyper_res).
% 1.71/1.91 dependent: set(factor).
% 1.71/1.91 dependent: set(unit_deletion).
% 1.71/1.91
% 1.71/1.91 ------------> process usable:
% 1.71/1.91 ** KEPT (pick-wt=2): 1 [] -f(exist).
% 1.71/1.91 ** KEPT (pick-wt=6): 2 [] c(A)|d(A)| -a(A).
% 1.71/1.91 ** KEPT (pick-wt=4): 3 [] a(A)| -d(A).
% 1.71/1.91 ** KEPT (pick-wt=4): 4 [] a(A)| -c(A).
% 1.71/1.91 ** KEPT (pick-wt=15): 5 [] e_qualish(A,B)| -e(C)| -r(C,A)| -r(C,B)| -c(A)| -c(B).
% 1.71/1.91 ** KEPT (pick-wt=4): 6 [] r3least(A)| -e(A).
% 1.71/1.91 ** KEPT (pick-wt=7): 7 [] a(A)| -e(B)| -r(B,A).
% 1.71/1.91 ** KEPT (pick-wt=12): 8 [] e(A)| -a(u1r1(A))| -r3least(A)| -e_qualish(u1r3(A),u1r2(A)).
% 1.71/1.91 ** KEPT (pick-wt=10): 9 [] e(A)|c(u1r2(A))| -a(u1r1(A))| -r3least(A).
% 1.71/1.91 ** KEPT (pick-wt=10): 10 [] e(A)|c(u1r3(A))| -a(u1r1(A))| -r3least(A).
% 1.71/1.91 ** KEPT (pick-wt=11): 11 [] e(A)|r(A,u1r2(A))| -a(u1r1(A))| -r3least(A).
% 1.71/1.91 ** KEPT (pick-wt=11): 12 [] e(A)|r(A,u1r3(A))| -a(u1r1(A))| -r3least(A).
% 1.71/1.91 ** KEPT (pick-wt=13): 13 [] e(A)|r(A,u1r1(A))| -r3least(A)| -e_qualish(u1r3(A),u1r2(A)).
% 1.71/1.91 ** KEPT (pick-wt=11): 14 [] e(A)|r(A,u1r1(A))|c(u1r2(A))| -r3least(A).
% 1.71/1.91 ** KEPT (pick-wt=11): 15 [] e(A)|r(A,u1r1(A))|c(u1r3(A))| -r3least(A).
% 1.71/1.91 ** KEPT (pick-wt=12): 16 [] e(A)|r(A,u1r1(A))|r(A,u1r2(A))| -r3least(A).
% 1.71/1.91 ** KEPT (pick-wt=12): 17 [] e(A)|r(A,u1r1(A))|r(A,u1r3(A))| -r3least(A).
% 1.71/1.91 ** KEPT (pick-wt=7): 18 [] -r3least(A)| -e_qualish(u2r2(A),u2r1(A)).
% 1.71/1.91 ** KEPT (pick-wt=7): 19 [] -r3least(A)| -e_qualish(u2r3(A),u2r1(A)).
% 1.71/1.91 ** KEPT (pick-wt=7): 20 [] -r3least(A)| -e_qualish(u2r3(A),u2r2(A)).
% 1.71/1.91 ** KEPT (pick-wt=6): 21 [] r(A,u2r1(A))| -r3least(A).
% 1.71/1.91 ** KEPT (pick-wt=6): 22 [] r(A,u2r2(A))| -r3least(A).
% 1.71/1.91 ** KEPT (pick-wt=6): 23 [] r(A,u2r3(A))| -r3least(A).
% 1.71/1.91 ** KEPT (pick-wt=20): 24 [] r3least(A)|e_qualish(B,C)|e_qualish(B,D)|e_qualish(C,D)| -r(A,B)| -r(A,C)| -r(A,D).
% 1.71/1.91 ** KEPT (pick-wt=5): 25 [] d(u3r1(A))| -f(A).
% 1.71/1.91 ** KEPT (pick-wt=5): 26 [] d(u3r2(A))| -f(A).
% 1.71/1.91 ** KEPT (pick-wt=7): 27 [] -f(A)| -e_qualish(u3r2(A),u3r1(A)).
% 1.71/1.92 ** KEPT (pick-wt=6): 28 [] r(A,u3r1(A))| -f(A).
% 1.71/1.92 ** KEPT (pick-wt=6): 29 [] r(A,u3r2(A))| -f(A).
% 1.71/1.92 ** KEPT (pick-wt=15): 30 [] f(A)|e_qualish(B,C)| -r(A,B)| -r(A,C)| -d(B)| -d(C).
% 1.71/1.92
% 1.71/1.92 ------------> process sos:
% 1.71/1.92 ** KEPT (pick-wt=2): 34 [] e(exist).
% 1.71/1.92
% 1.71/1.92 ======= end of input processing =======
% 1.71/1.92
% 1.71/1.92 =========== start of search ===========
% 1.71/1.92
% 1.71/1.92 -------- PROOF --------
% 1.71/1.92
% 1.71/1.92 -----> EMPTY CLAUSE at 0.01 sec ----> 95 [hyper,93,20,35] $F.
% 1.71/1.92
% 1.71/1.92 Length of proof is 18. Level of proof is 9.
% 1.71/1.92
% 1.71/1.92 ---------------- PROOF ----------------
% 1.71/1.92 % SZS status Unsatisfiable
% 1.71/1.92 % SZS output start Refutation
% See solution above
% 1.71/1.92 ------------ end of proof -------------
% 1.71/1.92
% 1.71/1.92
% 1.71/1.92 Search stopped by max_proofs option.
% 1.71/1.92
% 1.71/1.92
% 1.71/1.92 Search stopped by max_proofs option.
% 1.71/1.92
% 1.71/1.92 ============ end of search ============
% 1.71/1.92
% 1.71/1.92 -------------- statistics -------------
% 1.71/1.92 clauses given 35
% 1.71/1.92 clauses generated 492
% 1.71/1.92 clauses kept 94
% 1.71/1.92 clauses forward subsumed 428
% 1.71/1.92 clauses back subsumed 41
% 1.71/1.92 Kbytes malloced 976
% 1.71/1.92
% 1.71/1.92 ----------- times (seconds) -----------
% 1.71/1.92 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.71/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.71/1.92
% 1.71/1.92 That finishes the proof of the theorem.
% 1.71/1.92
% 1.71/1.92 Process 2454 finished Wed Jul 27 03:28:23 2022
% 1.71/1.92 Otter interrupted
% 1.71/1.92 PROOF FOUND
%------------------------------------------------------------------------------