%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN015-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:23:19 EDT 2022
% Result : Unsatisfiable 1.81s 2.02s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of clauses : 29 ( 11 unt; 13 nHn; 28 RR)
% Number of literals : 70 ( 0 equ; 16 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ e_qualish(A,B)
| e_qualish(B,A) ),
file('SYN015-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ e_qualish(A,B)
| ~ e_qualish(B,C)
| e_qualish(A,C) ),
file('SYN015-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ e_qualish(A,B)
| ~ element(C,A)
| element(C,B) ),
file('SYN015-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ e_qualish(f(A),m)
| ~ element(A,m)
| e_qualish(A,m) ),
file('SYN015-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ e_qualish(f(A),A)
| ~ element(A,m)
| e_qualish(A,m) ),
file('SYN015-2.p',unknown),
[] ).
cnf(9,axiom,
( element(A,f(A))
| ~ element(A,m)
| e_qualish(A,m) ),
file('SYN015-2.p',unknown),
[] ).
cnf(10,axiom,
( element(f(A),A)
| ~ element(A,m)
| e_qualish(A,m) ),
file('SYN015-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ element(A,B)
| ~ element(B,A)
| e_qualish(A,B)
| e_qualish(A,m)
| element(B,m)
| e_qualish(B,m) ),
file('SYN015-2.p',unknown),
[] ).
cnf(16,axiom,
( ~ e_qualish(A,n)
| element(A,k)
| e_qualish(A,k) ),
file('SYN015-2.p',unknown),
[] ).
cnf(17,axiom,
( ~ element(A,k)
| e_qualish(A,n)
| e_qualish(A,m)
| e_qualish(A,k) ),
file('SYN015-2.p',unknown),
[] ).
cnf(20,axiom,
~ e_qualish(n,k),
file('SYN015-2.p',unknown),
[] ).
cnf(28,axiom,
e_qualish(A,A),
file('SYN015-2.p',unknown),
[] ).
cnf(31,axiom,
e_qualish(m,k),
file('SYN015-2.p',unknown),
[] ).
cnf(32,plain,
element(n,k),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[28,16]),20]),
[iquote('hyper,28,16,unit_del,20')] ).
cnf(35,plain,
e_qualish(k,m),
inference(hyper,[status(thm)],[31,1]),
[iquote('hyper,31,1')] ).
cnf(40,plain,
element(n,m),
inference(hyper,[status(thm)],[35,3,32]),
[iquote('hyper,35,3,32')] ).
cnf(41,plain,
( element(f(n),n)
| e_qualish(n,m) ),
inference(hyper,[status(thm)],[40,10]),
[iquote('hyper,40,10')] ).
cnf(42,plain,
( element(n,f(n))
| e_qualish(n,m) ),
inference(hyper,[status(thm)],[40,9]),
[iquote('hyper,40,9')] ).
cnf(60,plain,
( e_qualish(n,m)
| e_qualish(n,f(n))
| element(f(n),m)
| e_qualish(f(n),m) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[42,11,41])])]),
[iquote('hyper,42,11,41,factor_simp,factor_simp')] ).
cnf(117,plain,
( e_qualish(n,m)
| e_qualish(n,f(n))
| e_qualish(f(n),m)
| element(f(n),k) ),
inference(hyper,[status(thm)],[60,3,31]),
[iquote('hyper,60,3,31')] ).
cnf(135,plain,
( e_qualish(n,m)
| e_qualish(n,f(n))
| e_qualish(f(n),m)
| e_qualish(f(n),n)
| e_qualish(f(n),k) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[117,17])]),
[iquote('hyper,117,17,factor_simp')] ).
cnf(281,plain,
( e_qualish(n,m)
| e_qualish(f(n),m)
| e_qualish(f(n),n)
| e_qualish(f(n),k) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[135,1])]),
[iquote('hyper,135,1,factor_simp')] ).
cnf(320,plain,
( e_qualish(n,m)
| e_qualish(f(n),n)
| e_qualish(f(n),k) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[281,7,40])]),
[iquote('hyper,281,7,40,factor_simp')] ).
cnf(355,plain,
( e_qualish(n,m)
| e_qualish(f(n),k) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[320,8,40])]),
[iquote('hyper,320,8,40,factor_simp')] ).
cnf(384,plain,
e_qualish(f(n),k),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[355,2,31]),20]),
[iquote('hyper,355,2,31,unit_del,20')] ).
cnf(408,plain,
e_qualish(f(n),m),
inference(hyper,[status(thm)],[384,2,35]),
[iquote('hyper,384,2,35')] ).
cnf(410,plain,
e_qualish(n,m),
inference(hyper,[status(thm)],[408,7,40]),
[iquote('hyper,408,7,40')] ).
cnf(441,plain,
e_qualish(n,k),
inference(hyper,[status(thm)],[410,2,31]),
[iquote('hyper,410,2,31')] ).
cnf(442,plain,
$false,
inference(binary,[status(thm)],[441,20]),
[iquote('binary,441.1,20.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN015-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 11:24:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.89 ----- Otter 3.3f, August 2004 -----
% 1.70/1.89 The process was started by sandbox on n018.cluster.edu,
% 1.70/1.89 Wed Jul 27 11:24:16 2022
% 1.70/1.89 The command was "./otter". The process ID is 5668.
% 1.70/1.89
% 1.70/1.89 set(prolog_style_variables).
% 1.70/1.89 set(auto).
% 1.70/1.89 dependent: set(auto1).
% 1.70/1.89 dependent: set(process_input).
% 1.70/1.89 dependent: clear(print_kept).
% 1.70/1.89 dependent: clear(print_new_demod).
% 1.70/1.89 dependent: clear(print_back_demod).
% 1.70/1.89 dependent: clear(print_back_sub).
% 1.70/1.89 dependent: set(control_memory).
% 1.70/1.89 dependent: assign(max_mem, 12000).
% 1.70/1.89 dependent: assign(pick_given_ratio, 4).
% 1.70/1.89 dependent: assign(stats_level, 1).
% 1.70/1.89 dependent: assign(max_seconds, 10800).
% 1.70/1.89 clear(print_given).
% 1.70/1.89
% 1.70/1.89 list(usable).
% 1.70/1.89 0 [] e_qualish(X,X).
% 1.70/1.89 0 [] -e_qualish(X,Y)|e_qualish(Y,X).
% 1.70/1.89 0 [] -e_qualish(X,Y)| -e_qualish(Y,Z)|e_qualish(X,Z).
% 1.70/1.89 0 [] -e_qualish(A,B)| -element(C,A)|element(C,B).
% 1.70/1.89 0 [] -element(A,B)| -e_qualish(A,C)|element(C,B).
% 1.70/1.89 0 [] -element(A,a)|e_qualish(A,k)|e_qualish(A,a).
% 1.70/1.89 0 [] -e_qualish(A,k)|element(A,a)|e_qualish(A,a).
% 1.70/1.89 0 [] -e_qualish(f(A),m)| -element(A,m)|e_qualish(A,m).
% 1.70/1.89 0 [] -e_qualish(f(A),A)| -element(A,m)|e_qualish(A,m).
% 1.70/1.89 0 [] element(A,f(A))| -element(A,m)|e_qualish(A,m).
% 1.70/1.89 0 [] element(f(A),A)| -element(A,m)|e_qualish(A,m).
% 1.70/1.89 0 [] -element(A,B)| -element(B,A)|e_qualish(A,B)|e_qualish(A,m)|element(B,m)|e_qualish(B,m).
% 1.70/1.89 0 [] -e_qualish(g(A),n)|element(A,n)|e_qualish(A,n).
% 1.70/1.89 0 [] -e_qualish(g(A),A)|element(A,n)|e_qualish(A,n).
% 1.70/1.89 0 [] element(A,g(A))|element(A,n)|e_qualish(A,n).
% 1.70/1.89 0 [] element(g(A),A)|element(A,n)|e_qualish(A,n).
% 1.70/1.89 0 [] -element(A,B)| -element(B,A)|e_qualish(A,B)|e_qualish(A,n)| -element(B,n)|e_qualish(B,n).
% 1.70/1.89 0 [] -e_qualish(A,m)|element(A,k)|e_qualish(A,k).
% 1.70/1.89 0 [] -e_qualish(A,n)|element(A,k)|e_qualish(A,k).
% 1.70/1.89 0 [] -element(A,k)|e_qualish(A,n)|e_qualish(A,m)|e_qualish(A,k).
% 1.70/1.89 0 [] -e_qualish(n,a).
% 1.70/1.89 0 [] -e_qualish(m,n).
% 1.70/1.89 0 [] -e_qualish(n,k).
% 1.70/1.89 0 [] -e_qualish(m,a).
% 1.70/1.89 0 [] -e_qualish(k,a).
% 1.70/1.89 0 [] e_qualish(m,k).
% 1.70/1.89 end_of_list.
% 1.70/1.89
% 1.70/1.89 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.70/1.89
% 1.70/1.89 This is a non-Horn set without equality. The strategy will
% 1.70/1.89 be ordered hyper_res, unit deletion, and factoring, with
% 1.70/1.89 satellites in sos and with nuclei in usable.
% 1.70/1.89
% 1.70/1.89 dependent: set(hyper_res).
% 1.70/1.89 dependent: set(factor).
% 1.70/1.89 dependent: set(unit_deletion).
% 1.70/1.89
% 1.70/1.89 ------------> process usable:
% 1.70/1.89 ** KEPT (pick-wt=6): 1 [] -e_qualish(A,B)|e_qualish(B,A).
% 1.70/1.89 ** KEPT (pick-wt=9): 2 [] -e_qualish(A,B)| -e_qualish(B,C)|e_qualish(A,C).
% 1.70/1.89 ** KEPT (pick-wt=9): 3 [] -e_qualish(A,B)| -element(C,A)|element(C,B).
% 1.70/1.89 ** KEPT (pick-wt=9): 4 [] -element(A,B)| -e_qualish(A,C)|element(C,B).
% 1.70/1.89 ** KEPT (pick-wt=9): 5 [] -element(A,a)|e_qualish(A,k)|e_qualish(A,a).
% 1.70/1.89 ** KEPT (pick-wt=9): 6 [] -e_qualish(A,k)|element(A,a)|e_qualish(A,a).
% 1.70/1.89 ** KEPT (pick-wt=10): 7 [] -e_qualish(f(A),m)| -element(A,m)|e_qualish(A,m).
% 1.70/1.89 ** KEPT (pick-wt=10): 8 [] -e_qualish(f(A),A)| -element(A,m)|e_qualish(A,m).
% 1.70/1.89 ** KEPT (pick-wt=10): 9 [] element(A,f(A))| -element(A,m)|e_qualish(A,m).
% 1.70/1.89 ** KEPT (pick-wt=10): 10 [] element(f(A),A)| -element(A,m)|e_qualish(A,m).
% 1.70/1.89 ** KEPT (pick-wt=18): 11 [] -element(A,B)| -element(B,A)|e_qualish(A,B)|e_qualish(A,m)|element(B,m)|e_qualish(B,m).
% 1.70/1.89 ** KEPT (pick-wt=10): 12 [] -e_qualish(g(A),n)|element(A,n)|e_qualish(A,n).
% 1.70/1.89 ** KEPT (pick-wt=10): 13 [] -e_qualish(g(A),A)|element(A,n)|e_qualish(A,n).
% 1.70/1.89 ** KEPT (pick-wt=18): 14 [] -element(A,B)| -element(B,A)|e_qualish(A,B)|e_qualish(A,n)| -element(B,n)|e_qualish(B,n).
% 1.70/1.89 ** KEPT (pick-wt=9): 15 [] -e_qualish(A,m)|element(A,k)|e_qualish(A,k).
% 1.70/1.89 ** KEPT (pick-wt=9): 16 [] -e_qualish(A,n)|element(A,k)|e_qualish(A,k).
% 1.70/1.89 ** KEPT (pick-wt=12): 17 [] -element(A,k)|e_qualish(A,n)|e_qualish(A,m)|e_qualish(A,k).
% 1.70/1.89 ** KEPT (pick-wt=3): 18 [] -e_qualish(n,a).
% 1.70/1.89 ** KEPT (pick-wt=3): 19 [] -e_qualish(m,n).
% 1.70/1.89 ** KEPT (pick-wt=3): 20 [] -e_qualish(n,k).
% 1.70/1.89 ** KEPT (pick-wt=3): 21 [] -e_qualish(m,a).
% 1.70/1.89 ** KEPT (pick-wt=3): 22 [] -e_qualish(k,a).
% 1.70/1.89
% 1.70/1.89 ------------> process sos:
% 1.70/1.89 ** KEPT (pick-wt=3): 28 [] e_qualish(A,A).
% 1.70/1.89 ** KEPT (pick-wt=10): 29 [] element(A,g(A))|element(A,n)|e_qualish(A,n).
% 1.70/1.89 ** KEPT (pick-wt=10): 30 [] element(g(A),A)|element(A,n)|e_qualish(A,n).
% 1.70/1.89 ** KEPT (pick-wt=3): 31 [] e_qualish(m,k).
% 1.70/1.89 28 back subsumes 27.
% 1.70/1.89 28 back subsumes 26.
% 1.70/1.89 28 back subsumes 25.
% 1.81/2.02 28 back subsumes 24.
% 1.81/2.02 28 back subsumes 23.
% 1.81/2.02
% 1.81/2.02 ======= end of input processing =======
% 1.81/2.02
% 1.81/2.02 =========== start of search ===========
% 1.81/2.02
% 1.81/2.02 -------- PROOF --------
% 1.81/2.02
% 1.81/2.02 ----> UNIT CONFLICT at 0.13 sec ----> 442 [binary,441.1,20.1] $F.
% 1.81/2.02
% 1.81/2.02 Length of proof is 15. Level of proof is 13.
% 1.81/2.02
% 1.81/2.02 ---------------- PROOF ----------------
% 1.81/2.02 % SZS status Unsatisfiable
% 1.81/2.02 % SZS output start Refutation
% See solution above
% 1.81/2.02 ------------ end of proof -------------
% 1.81/2.02
% 1.81/2.02
% 1.81/2.02 Search stopped by max_proofs option.
% 1.81/2.02
% 1.81/2.02
% 1.81/2.02 Search stopped by max_proofs option.
% 1.81/2.02
% 1.81/2.02 ============ end of search ============
% 1.81/2.02
% 1.81/2.02 -------------- statistics -------------
% 1.81/2.02 clauses given 59
% 1.81/2.02 clauses generated 5207
% 1.81/2.02 clauses kept 441
% 1.81/2.02 clauses forward subsumed 4787
% 1.81/2.02 clauses back subsumed 214
% 1.81/2.02 Kbytes malloced 976
% 1.81/2.02
% 1.81/2.02 ----------- times (seconds) -----------
% 1.81/2.02 user CPU time 0.13 (0 hr, 0 min, 0 sec)
% 1.81/2.02 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.02 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.81/2.02
% 1.81/2.02 That finishes the proof of the theorem.
% 1.81/2.02
% 1.81/2.02 Process 5668 finished Wed Jul 27 11:24:18 2022
% 1.81/2.03 Otter interrupted
% 1.81/2.03 PROOF FOUND
%------------------------------------------------------------------------------