%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : COL098-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 12:48:14 EDT 2022
% Result : Unsatisfiable 1.73s 1.91s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of clauses : 17 ( 10 unt; 0 nHn; 16 RR)
% Number of literals : 28 ( 0 equ; 12 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 17 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(10,axiom,
( ~ member(pair(A,B),C)
| member(pair(A,B),trancl(C)) ),
file('COL098-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ trans(A)
| ~ member(pair(B,C),A)
| ~ member(pair(C,D),A)
| member(pair(B,D),A) ),
file('COL098-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(pair(A,B),r)
| ~ member(pair(A,C),r)
| member(pair(B,sk1(A,B,C)),r) ),
file('COL098-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(pair(A,B),r)
| ~ member(pair(A,C),r)
| member(pair(C,sk1(A,B,C)),r) ),
file('COL098-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(pair(x,A),r)
| member(pair(A,sk2(A)),trancl(r)) ),
file('COL098-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ member(pair(x,A),r)
| member(pair(y,sk2(A)),r) ),
file('COL098-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ member(pair(sk3,A),trancl(r))
| ~ member(pair(z,A),r) ),
file('COL098-1.p',unknown),
[] ).
cnf(18,axiom,
trans(trancl(A)),
file('COL098-1.p',unknown),
[] ).
cnf(20,axiom,
member(pair(y,z),r),
file('COL098-1.p',unknown),
[] ).
cnf(21,axiom,
member(pair(x,sk3),r),
file('COL098-1.p',unknown),
[] ).
cnf(34,plain,
member(pair(y,sk2(sk3)),r),
inference(hyper,[status(thm)],[21,15]),
[iquote('hyper,21,15')] ).
cnf(35,plain,
member(pair(sk3,sk2(sk3)),trancl(r)),
inference(hyper,[status(thm)],[21,14]),
[iquote('hyper,21,14')] ).
cnf(75,plain,
member(pair(sk2(sk3),sk1(y,z,sk2(sk3))),r),
inference(hyper,[status(thm)],[34,13,20]),
[iquote('hyper,34,13,20')] ).
cnf(77,plain,
member(pair(z,sk1(y,z,sk2(sk3))),r),
inference(hyper,[status(thm)],[34,12,20]),
[iquote('hyper,34,12,20')] ).
cnf(656,plain,
member(pair(sk2(sk3),sk1(y,z,sk2(sk3))),trancl(r)),
inference(hyper,[status(thm)],[75,10]),
[iquote('hyper,75,10')] ).
cnf(1116,plain,
member(pair(sk3,sk1(y,z,sk2(sk3))),trancl(r)),
inference(hyper,[status(thm)],[656,11,18,35]),
[iquote('hyper,656,11,18,35')] ).
cnf(1138,plain,
$false,
inference(hyper,[status(thm)],[1116,16,77]),
[iquote('hyper,1116,16,77')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL098-1 : TPTP v8.1.0. Released v2.7.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 02:23:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.73/1.91 ----- Otter 3.3f, August 2004 -----
% 1.73/1.91 The process was started by sandbox2 on n005.cluster.edu,
% 1.73/1.91 Wed Jul 27 02:23:05 2022
% 1.73/1.91 The command was "./otter". The process ID is 19533.
% 1.73/1.91
% 1.73/1.91 set(prolog_style_variables).
% 1.73/1.91 set(auto).
% 1.73/1.91 dependent: set(auto1).
% 1.73/1.91 dependent: set(process_input).
% 1.73/1.91 dependent: clear(print_kept).
% 1.73/1.91 dependent: clear(print_new_demod).
% 1.73/1.91 dependent: clear(print_back_demod).
% 1.73/1.91 dependent: clear(print_back_sub).
% 1.73/1.91 dependent: set(control_memory).
% 1.73/1.91 dependent: assign(max_mem, 12000).
% 1.73/1.91 dependent: assign(pick_given_ratio, 4).
% 1.73/1.91 dependent: assign(stats_level, 1).
% 1.73/1.91 dependent: assign(max_seconds, 10800).
% 1.73/1.91 clear(print_given).
% 1.73/1.91
% 1.73/1.91 list(usable).
% 1.73/1.91 0 [] A=A.
% 1.73/1.91 0 [] combK!=combS.
% 1.73/1.91 0 [] combK!=comb_app(P,Q).
% 1.73/1.91 0 [] combS!=comb_app(P,Q).
% 1.73/1.91 0 [] comb_app(P1,Q1)!=comb_app(P2,Q2)|P1=P2.
% 1.73/1.91 0 [] comb_app(P1,Q1)!=comb_app(P2,Q2)|Q1=Q2.
% 1.73/1.91 0 [] P1!=P2|Q1!=Q2|comb_app(P1,Q1)=comb_app(P2,Q2).
% 1.73/1.91 0 [] -member(pair(A,B),R)|member(pair(A,B),trancl(R)).
% 1.73/1.91 0 [] trans(trancl(R)).
% 1.73/1.91 0 [] -trans(R)| -member(pair(A,B),R)| -member(pair(B,C),R)|member(pair(A,C),R).
% 1.73/1.91 0 [] -member(pair(X,Y),r)| -member(pair(X,YP),r)|member(pair(Y,sk1(X,Y,YP)),r).
% 1.73/1.91 0 [] -member(pair(X,Y),r)| -member(pair(X,YP),r)|member(pair(YP,sk1(X,Y,YP)),r).
% 1.73/1.91 0 [] member(pair(x,y),trancl(r)).
% 1.73/1.91 0 [] member(pair(y,z),r).
% 1.73/1.91 0 [] -member(pair(x,YP),r)|member(pair(YP,sk2(YP)),trancl(r)).
% 1.73/1.91 0 [] -member(pair(x,YP),r)|member(pair(y,sk2(YP)),r).
% 1.73/1.91 0 [] member(pair(x,sk3),r).
% 1.73/1.91 0 [] -member(pair(sk3,ZA),trancl(r))| -member(pair(z,ZA),r).
% 1.73/1.91 end_of_list.
% 1.73/1.91
% 1.73/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.73/1.91
% 1.73/1.91 This is a Horn set with equality. The strategy will be
% 1.73/1.91 Knuth-Bendix and hyper_res, with positive clauses in
% 1.73/1.91 sos and nonpositive clauses in usable.
% 1.73/1.91
% 1.73/1.91 dependent: set(knuth_bendix).
% 1.73/1.91 dependent: set(anl_eq).
% 1.73/1.91 dependent: set(para_from).
% 1.73/1.91 dependent: set(para_into).
% 1.73/1.91 dependent: clear(para_from_right).
% 1.73/1.91 dependent: clear(para_into_right).
% 1.73/1.91 dependent: set(para_from_vars).
% 1.73/1.91 dependent: set(eq_units_both_ways).
% 1.73/1.91 dependent: set(dynamic_demod_all).
% 1.73/1.91 dependent: set(dynamic_demod).
% 1.73/1.91 dependent: set(order_eq).
% 1.73/1.91 dependent: set(back_demod).
% 1.73/1.91 dependent: set(lrpo).
% 1.73/1.91 dependent: set(hyper_res).
% 1.73/1.91 dependent: clear(order_hyper).
% 1.73/1.91
% 1.73/1.91 ------------> process usable:
% 1.73/1.91 ** KEPT (pick-wt=3): 2 [copy,1,flip.1] combS!=combK.
% 1.73/1.91 ** KEPT (pick-wt=5): 4 [copy,3,flip.1] comb_app(A,B)!=combK.
% 1.73/1.91 ** KEPT (pick-wt=5): 6 [copy,5,flip.1] comb_app(A,B)!=combS.
% 1.73/1.91 ** KEPT (pick-wt=10): 7 [] comb_app(A,B)!=comb_app(C,D)|A=C.
% 1.73/1.91 ** KEPT (pick-wt=10): 8 [] comb_app(A,B)!=comb_app(C,D)|B=D.
% 1.73/1.91 ** KEPT (pick-wt=13): 9 [] A!=B|C!=D|comb_app(A,C)=comb_app(B,D).
% 1.73/1.91 ** KEPT (pick-wt=11): 10 [] -member(pair(A,B),C)|member(pair(A,B),trancl(C)).
% 1.73/1.91 ** KEPT (pick-wt=17): 11 [] -trans(A)| -member(pair(B,C),A)| -member(pair(C,D),A)|member(pair(B,D),A).
% 1.73/1.91 ** KEPT (pick-wt=18): 12 [] -member(pair(A,B),r)| -member(pair(A,C),r)|member(pair(B,sk1(A,B,C)),r).
% 1.73/1.91 ** KEPT (pick-wt=18): 13 [] -member(pair(A,B),r)| -member(pair(A,C),r)|member(pair(C,sk1(A,B,C)),r).
% 1.73/1.91 ** KEPT (pick-wt=12): 14 [] -member(pair(x,A),r)|member(pair(A,sk2(A)),trancl(r)).
% 1.73/1.91 ** KEPT (pick-wt=11): 15 [] -member(pair(x,A),r)|member(pair(y,sk2(A)),r).
% 1.73/1.91 ** KEPT (pick-wt=11): 16 [] -member(pair(sk3,A),trancl(r))| -member(pair(z,A),r).
% 1.73/1.91
% 1.73/1.91 ------------> process sos:
% 1.73/1.91 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.73/1.91 ** KEPT (pick-wt=3): 18 [] trans(trancl(A)).
% 1.73/1.91 ** KEPT (pick-wt=6): 19 [] member(pair(x,y),trancl(r)).
% 1.73/1.91 ** KEPT (pick-wt=5): 20 [] member(pair(y,z),r).
% 1.73/1.91 ** KEPT (pick-wt=5): 21 [] member(pair(x,sk3),r).
% 1.73/1.91 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.73/1.91
% 1.73/1.91 ======= end of input processing =======
% 1.73/1.91
% 1.73/1.91 =========== start of search ===========
% 1.73/1.91
% 1.73/1.91 -------- PROOF --------
% 1.73/1.91
% 1.73/1.91 -----> EMPTY CLAUSE at 0.02 sec ----> 1138 [hyper,1116,16,77] $F.
% 1.73/1.91
% 1.73/1.91 Length of proof is 6. Level of proof is 4.
% 1.73/1.91
% 1.73/1.91 ---------------- PROOF ----------------
% 1.73/1.91 % SZS status Unsatisfiable
% 1.73/1.91 % SZS output start Refutation
% See solution above
% 1.73/1.91 ------------ end of proof -------------
% 1.73/1.91
% 1.73/1.91
% 1.73/1.91 Search stopped by max_proofs option.
% 1.73/1.91
% 1.73/1.91
% 1.73/1.91 Search stopped by max_proofs option.
% 1.73/1.91
% 1.73/1.91 ============ end of search ============
% 1.73/1.91
% 1.73/1.91 -------------- statistics -------------
% 1.73/1.91 clauses given 75
% 1.73/1.91 clauses generated 1210
% 1.73/1.91 clauses kept 1134
% 1.73/1.91 clauses forward subsumed 94
% 1.73/1.91 clauses back subsumed 0
% 1.73/1.91 Kbytes malloced 1953
% 1.73/1.91
% 1.73/1.91 ----------- times (seconds) -----------
% 1.73/1.91 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.73/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.91 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.73/1.91
% 1.73/1.91 That finishes the proof of the theorem.
% 1.73/1.91
% 1.73/1.91 Process 19533 finished Wed Jul 27 02:23:07 2022
% 1.73/1.91 Otter interrupted
% 1.73/1.91 PROOF FOUND
%------------------------------------------------------------------------------