%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS013-1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:00:58 EDT 2022
% Result : Unsatisfiable 1.95s 2.15s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 33 ( 11 unt; 12 nHn; 28 RR)
% Number of literals : 62 ( 0 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ f(exist),
file('KRS013-1.p',unknown),
[] ).
cnf(2,axiom,
( t2least(A)
| ~ c(A) ),
file('KRS013-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ t2least(A)
| ~ e_qualish(u1r2(A),u1r1(A)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(5,axiom,
( t(A,u1r1(A))
| ~ t2least(A) ),
file('KRS013-1.p',unknown),
[] ).
cnf(6,axiom,
( t(A,u1r2(A))
| ~ t2least(A) ),
file('KRS013-1.p',unknown),
[] ).
cnf(8,axiom,
( t1most(A)
| ~ d(A) ),
file('KRS013-1.p',unknown),
[] ).
cnf(10,axiom,
( e_qualish(A,B)
| ~ t1most(C)
| ~ t(C,A)
| ~ t(C,B) ),
file('KRS013-1.p',unknown),
[] ).
cnf(12,axiom,
( d(A)
| ~ e(B)
| ~ r(B,A) ),
file('KRS013-1.p',unknown),
[] ).
cnf(13,axiom,
( c(A)
| ~ e(B)
| ~ r(B,A)
| ~ s2least(A) ),
file('KRS013-1.p',unknown),
[] ).
cnf(21,axiom,
( s2least(A)
| e_qualish(B,C)
| ~ s(A,B)
| ~ s(A,C) ),
file('KRS013-1.p',unknown),
[] ).
cnf(23,axiom,
( f(A)
| ~ s1most(u6r1(A)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(25,axiom,
( s1most(A)
| ~ e_qualish(u7r2(A),u7r1(A)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(30,axiom,
e(exist),
file('KRS013-1.p',unknown),
[] ).
cnf(35,axiom,
( f(A)
| r(A,u6r1(A)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(36,axiom,
( s1most(A)
| s(A,u7r1(A)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(37,axiom,
( s1most(A)
| s(A,u7r2(A)) ),
file('KRS013-1.p',unknown),
[] ).
cnf(40,plain,
r(exist,u6r1(exist)),
inference(hyper,[status(thm)],[35,1]),
[iquote('hyper,35,1')] ).
cnf(41,plain,
d(u6r1(exist)),
inference(hyper,[status(thm)],[40,12,30]),
[iquote('hyper,40,12,30')] ).
cnf(44,plain,
t1most(u6r1(exist)),
inference(hyper,[status(thm)],[41,8]),
[iquote('hyper,41,8')] ).
cnf(45,plain,
( s(u6r1(A),u7r1(u6r1(A)))
| f(A) ),
inference(hyper,[status(thm)],[36,23]),
[iquote('hyper,36,23')] ).
cnf(46,plain,
( s(u6r1(A),u7r2(u6r1(A)))
| f(A) ),
inference(hyper,[status(thm)],[37,23]),
[iquote('hyper,37,23')] ).
cnf(51,plain,
s(u6r1(exist),u7r1(u6r1(exist))),
inference(hyper,[status(thm)],[45,1]),
[iquote('hyper,45,1')] ).
cnf(54,plain,
s(u6r1(exist),u7r2(u6r1(exist))),
inference(hyper,[status(thm)],[46,1]),
[iquote('hyper,46,1')] ).
cnf(57,plain,
( s2least(u6r1(exist))
| e_qualish(u7r2(u6r1(exist)),u7r1(u6r1(exist))) ),
inference(hyper,[status(thm)],[54,21,51]),
[iquote('hyper,54,21,51')] ).
cnf(79,plain,
( e_qualish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))
| c(u6r1(exist)) ),
inference(hyper,[status(thm)],[57,13,30,40]),
[iquote('hyper,57,13,30,40')] ).
cnf(83,plain,
( e_qualish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))
| t2least(u6r1(exist)) ),
inference(hyper,[status(thm)],[79,2]),
[iquote('hyper,79,2')] ).
cnf(92,plain,
( e_qualish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))
| t(u6r1(exist),u1r2(u6r1(exist))) ),
inference(hyper,[status(thm)],[83,6]),
[iquote('hyper,83,6')] ).
cnf(93,plain,
( e_qualish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))
| t(u6r1(exist),u1r1(u6r1(exist))) ),
inference(hyper,[status(thm)],[83,5]),
[iquote('hyper,83,5')] ).
cnf(110,plain,
( e_qualish(u7r2(u6r1(exist)),u7r1(u6r1(exist)))
| e_qualish(u1r2(u6r1(exist)),u1r1(u6r1(exist))) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[93,10,44,92])]),
[iquote('hyper,93,10,44,92,factor_simp')] ).
cnf(126,plain,
e_qualish(u7r2(u6r1(exist)),u7r1(u6r1(exist))),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[110,4,83])]),
[iquote('hyper,110,4,83,factor_simp')] ).
cnf(127,plain,
s1most(u6r1(exist)),
inference(hyper,[status(thm)],[126,25]),
[iquote('hyper,126,25')] ).
cnf(128,plain,
f(exist),
inference(hyper,[status(thm)],[127,23]),
[iquote('hyper,127,23')] ).
cnf(129,plain,
$false,
inference(binary,[status(thm)],[128,1]),
[iquote('binary,128.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS013-1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 03:33:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.14 ----- Otter 3.3f, August 2004 -----
% 1.95/2.14 The process was started by sandbox2 on n020.cluster.edu,
% 1.95/2.14 Wed Jul 27 03:33:53 2022
% 1.95/2.14 The command was "./otter". The process ID is 3241.
% 1.95/2.14
% 1.95/2.14 set(prolog_style_variables).
% 1.95/2.14 set(auto).
% 1.95/2.14 dependent: set(auto1).
% 1.95/2.14 dependent: set(process_input).
% 1.95/2.14 dependent: clear(print_kept).
% 1.95/2.14 dependent: clear(print_new_demod).
% 1.95/2.14 dependent: clear(print_back_demod).
% 1.95/2.14 dependent: clear(print_back_sub).
% 1.95/2.14 dependent: set(control_memory).
% 1.95/2.14 dependent: assign(max_mem, 12000).
% 1.95/2.14 dependent: assign(pick_given_ratio, 4).
% 1.95/2.14 dependent: assign(stats_level, 1).
% 1.95/2.14 dependent: assign(max_seconds, 10800).
% 1.95/2.14 clear(print_given).
% 1.95/2.14
% 1.95/2.14 list(usable).
% 1.95/2.14 0 [] e(exist).
% 1.95/2.14 0 [] -f(exist).
% 1.95/2.14 0 [] t2least(X1)| -c(X1).
% 1.95/2.14 0 [] c(X1)| -t2least(X1).
% 1.95/2.14 0 [] -t2least(X1)| -e_qualish(u1r2(X1),u1r1(X1)).
% 1.95/2.14 0 [] t(X1,u1r1(X1))| -t2least(X1).
% 1.95/2.14 0 [] t(X1,u1r2(X1))| -t2least(X1).
% 1.95/2.14 0 [] t2least(X1)|e_qualish(X3,X2)| -t(X1,X3)| -t(X1,X2).
% 1.95/2.14 0 [] t1most(X1)| -d(X1).
% 1.95/2.14 0 [] d(X1)| -t1most(X1).
% 1.95/2.14 0 [] e_qualish(X3,X2)| -t1most(X1)| -t(X1,X3)| -t(X1,X2).
% 1.95/2.14 0 [] t1most(X1)| -e_qualish(u3r2(X1),u3r1(X1)).
% 1.95/2.14 0 [] t1most(X1)|t(X1,u3r1(X1)).
% 1.95/2.14 0 [] t1most(X1)|t(X1,u3r2(X1)).
% 1.95/2.14 0 [] d(X3)| -e(X1)| -r(X1,X3).
% 1.95/2.14 0 [] c(X2)| -e(X1)| -r(X1,X2)| -s2least(X2).
% 1.95/2.14 0 [] e(X1)| -c(u4r1(X1))| -d(u4r2(X1)).
% 1.95/2.14 0 [] e(X1)|r(X1,u4r2(X1))| -c(u4r1(X1)).
% 1.95/2.14 0 [] e(X1)|s2least(u4r1(X1))| -d(u4r2(X1)).
% 1.95/2.14 0 [] e(X1)|s2least(u4r1(X1))|r(X1,u4r2(X1)).
% 1.95/2.14 0 [] e(X1)|r(X1,u4r1(X1))| -d(u4r2(X1)).
% 1.95/2.14 0 [] e(X1)|r(X1,u4r1(X1))|r(X1,u4r2(X1)).
% 1.95/2.14 0 [] -s2least(X1)| -e_qualish(u5r2(X1),u5r1(X1)).
% 1.95/2.14 0 [] s(X1,u5r1(X1))| -s2least(X1).
% 1.95/2.14 0 [] s(X1,u5r2(X1))| -s2least(X1).
% 1.95/2.14 0 [] s2least(X1)|e_qualish(X3,X2)| -s(X1,X3)| -s(X1,X2).
% 1.95/2.14 0 [] s1most(X2)| -f(X1)| -r(X1,X2).
% 1.95/2.14 0 [] f(X1)| -s1most(u6r1(X1)).
% 1.95/2.14 0 [] f(X1)|r(X1,u6r1(X1)).
% 1.95/2.14 0 [] e_qualish(X3,X2)| -s1most(X1)| -s(X1,X3)| -s(X1,X2).
% 1.95/2.14 0 [] s1most(X1)| -e_qualish(u7r2(X1),u7r1(X1)).
% 1.95/2.14 0 [] s1most(X1)|s(X1,u7r1(X1)).
% 1.95/2.14 0 [] s1most(X1)|s(X1,u7r2(X1)).
% 1.95/2.14 end_of_list.
% 1.95/2.14
% 1.95/2.14 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.95/2.14
% 1.95/2.14 This is a non-Horn set without equality. The strategy will
% 1.95/2.14 be ordered hyper_res, unit deletion, and factoring, with
% 1.95/2.14 satellites in sos and with nuclei in usable.
% 1.95/2.14
% 1.95/2.14 dependent: set(hyper_res).
% 1.95/2.14 dependent: set(factor).
% 1.95/2.14 dependent: set(unit_deletion).
% 1.95/2.14
% 1.95/2.14 ------------> process usable:
% 1.95/2.14 ** KEPT (pick-wt=2): 1 [] -f(exist).
% 1.95/2.14 ** KEPT (pick-wt=4): 2 [] t2least(A)| -c(A).
% 1.95/2.14 ** KEPT (pick-wt=4): 3 [] c(A)| -t2least(A).
% 1.95/2.14 ** KEPT (pick-wt=7): 4 [] -t2least(A)| -e_qualish(u1r2(A),u1r1(A)).
% 1.95/2.14 ** KEPT (pick-wt=6): 5 [] t(A,u1r1(A))| -t2least(A).
% 1.95/2.14 ** KEPT (pick-wt=6): 6 [] t(A,u1r2(A))| -t2least(A).
% 1.95/2.14 ** KEPT (pick-wt=11): 7 [] t2least(A)|e_qualish(B,C)| -t(A,B)| -t(A,C).
% 1.95/2.14 ** KEPT (pick-wt=4): 8 [] t1most(A)| -d(A).
% 1.95/2.14 ** KEPT (pick-wt=4): 9 [] d(A)| -t1most(A).
% 1.95/2.14 ** KEPT (pick-wt=11): 10 [] e_qualish(A,B)| -t1most(C)| -t(C,A)| -t(C,B).
% 1.95/2.14 ** KEPT (pick-wt=7): 11 [] t1most(A)| -e_qualish(u3r2(A),u3r1(A)).
% 1.95/2.14 ** KEPT (pick-wt=7): 12 [] d(A)| -e(B)| -r(B,A).
% 1.95/2.14 ** KEPT (pick-wt=9): 13 [] c(A)| -e(B)| -r(B,A)| -s2least(A).
% 1.95/2.14 ** KEPT (pick-wt=8): 14 [] e(A)| -c(u4r1(A))| -d(u4r2(A)).
% 1.95/2.14 ** KEPT (pick-wt=9): 15 [] e(A)|r(A,u4r2(A))| -c(u4r1(A)).
% 1.95/2.14 ** KEPT (pick-wt=8): 16 [] e(A)|s2least(u4r1(A))| -d(u4r2(A)).
% 1.95/2.14 ** KEPT (pick-wt=9): 17 [] e(A)|r(A,u4r1(A))| -d(u4r2(A)).
% 1.95/2.14 ** KEPT (pick-wt=7): 18 [] -s2least(A)| -e_qualish(u5r2(A),u5r1(A)).
% 1.95/2.14 ** KEPT (pick-wt=6): 19 [] s(A,u5r1(A))| -s2least(A).
% 1.95/2.14 ** KEPT (pick-wt=6): 20 [] s(A,u5r2(A))| -s2least(A).
% 1.95/2.14 ** KEPT (pick-wt=11): 21 [] s2least(A)|e_qualish(B,C)| -s(A,B)| -s(A,C).
% 1.95/2.14 ** KEPT (pick-wt=7): 22 [] s1most(A)| -f(B)| -r(B,A).
% 1.95/2.14 ** KEPT (pick-wt=5): 23 [] f(A)| -s1most(u6r1(A)).
% 1.95/2.14 ** KEPT (pick-wt=11): 24 [] e_qualish(A,B)| -s1most(C)| -s(C,A)| -s(C,B).
% 1.95/2.14 ** KEPT (pick-wt=7): 25 [] s1most(A)| -e_qualish(u7r2(A),u7r1(A)).
% 1.95/2.14
% 1.95/2.14 ------------> process sos:
% 1.95/2.14 ** KEPT (pick-wt=2): 30 [] e(exist).
% 1.95/2.14 ** KEPT (pick-wt=6): 31 [] t1most(A)|t(A,u3r1(A)).
% 1.95/2.14 ** KEPT (pick-wt=6): 32 [] t1most(A)|t(A,u3r2(A)).
% 1.95/2.14 ** KEPT (pick-wt=9): 33 [] e(A)|s2least(u4r1(A))|r(A,u4r2(A)).
% 1.95/2.14 ** KEPT (pick-wt=10): 34 [] e(A)|r(A,u4r1(A))|r(A,u4r2(A)).
% 1.95/2.14 ** KEPT (pick-wt=6): 35 [] f(A)|r(A,u6r1(A)).
% 1.95/2.14 ** KEPT (pick-wt=6): 36 [] s1most(A)|s(A,u7r1(A)).
% 1.95/2.15 ** KEPT (pick-wt=6): 37 [] s1most(A)|s(A,u7r2(A)).
% 1.95/2.15
% 1.95/2.15 ======= end of input processing =======
% 1.95/2.15
% 1.95/2.15 =========== start of search ===========
% 1.95/2.15
% 1.95/2.15 -------- PROOF --------
% 1.95/2.15
% 1.95/2.15 ----> UNIT CONFLICT at 0.01 sec ----> 129 [binary,128.1,1.1] $F.
% 1.95/2.15
% 1.95/2.15 Length of proof is 16. Level of proof is 10.
% 1.95/2.15
% 1.95/2.15 ---------------- PROOF ----------------
% 1.95/2.15 % SZS status Unsatisfiable
% 1.95/2.15 % SZS output start Refutation
% See solution above
% 1.95/2.15 ------------ end of proof -------------
% 1.95/2.15
% 1.95/2.15
% 1.95/2.15 Search stopped by max_proofs option.
% 1.95/2.15
% 1.95/2.15
% 1.95/2.15 Search stopped by max_proofs option.
% 1.95/2.15
% 1.95/2.15 ============ end of search ============
% 1.95/2.15
% 1.95/2.15 -------------- statistics -------------
% 1.95/2.15 clauses given 76
% 1.95/2.15 clauses generated 845
% 1.95/2.15 clauses kept 128
% 1.95/2.15 clauses forward subsumed 750
% 1.95/2.15 clauses back subsumed 64
% 1.95/2.15 Kbytes malloced 976
% 1.95/2.15
% 1.95/2.15 ----------- times (seconds) -----------
% 1.95/2.15 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.95/2.15 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.15 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.95/2.15
% 1.95/2.15 That finishes the proof of the theorem.
% 1.95/2.15
% 1.95/2.15 Process 3241 finished Wed Jul 27 03:33:55 2022
% 1.95/2.15 Otter interrupted
% 1.95/2.15 PROOF FOUND
%------------------------------------------------------------------------------