TSTP Solution File: ALG011-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG011-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 12:45:53 EDT 2022
% Result : Unsatisfiable 1.72s 1.92s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 11 unt; 2 nHn; 14 RR)
% Number of literals : 27 ( 2 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c(A)
| ~ d(A) ),
file('ALG011-1.p',unknown),
[] ).
cnf(2,axiom,
( d(f(A,B))
| ~ c(A)
| ~ c(B) ),
file('ALG011-1.p',unknown),
[] ).
cnf(3,axiom,
( c(f(A,B))
| ~ d(A)
| ~ d(B) ),
file('ALG011-1.p',unknown),
[] ).
cnf(4,plain,
( d(f(A,A))
| ~ c(A) ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.2.3')] ).
cnf(5,plain,
( c(f(A,A))
| ~ d(A) ),
inference(factor,[status(thm)],[3]),
[iquote('factor,3.2.3')] ).
cnf(7,axiom,
f(A,f(B,C)) = f(f(A,B),C),
file('ALG011-1.p',unknown),
[] ).
cnf(9,plain,
f(f(A,B),C) = f(A,f(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(10,axiom,
( c(A)
| d(A) ),
file('ALG011-1.p',unknown),
[] ).
cnf(11,axiom,
c(a1),
file('ALG011-1.p',unknown),
[] ).
cnf(12,axiom,
d(a2),
file('ALG011-1.p',unknown),
[] ).
cnf(13,plain,
d(f(a1,a1)),
inference(hyper,[status(thm)],[11,4]),
[iquote('hyper,11,4')] ).
cnf(14,plain,
c(f(a2,a2)),
inference(hyper,[status(thm)],[12,5]),
[iquote('hyper,12,5')] ).
cnf(16,plain,
( c(A)
| c(f(a2,A)) ),
inference(hyper,[status(thm)],[10,3,12]),
[iquote('hyper,10,3,12')] ).
cnf(20,plain,
c(f(a2,f(a1,a1))),
inference(hyper,[status(thm)],[13,3,12]),
[iquote('hyper,13,3,12')] ).
cnf(30,plain,
d(f(a2,f(a2,a1))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[14,2,11]),9]),
[iquote('hyper,14,2,11,demod,9')] ).
cnf(348,plain,
c(f(a2,a1)),
inference(hyper,[status(thm)],[30,1,16]),
[iquote('hyper,30,1,16')] ).
cnf(403,plain,
d(f(a2,f(a1,a1))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[348,2,11]),9]),
[iquote('hyper,348,2,11,demod,9')] ).
cnf(428,plain,
$false,
inference(hyper,[status(thm)],[403,1,20]),
[iquote('hyper,403,1,20')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG011-1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 03:02:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.92 ----- Otter 3.3f, August 2004 -----
% 1.72/1.92 The process was started by sandbox2 on n017.cluster.edu,
% 1.72/1.92 Wed Jul 27 03:02:33 2022
% 1.72/1.92 The command was "./otter". The process ID is 31001.
% 1.72/1.92
% 1.72/1.92 set(prolog_style_variables).
% 1.72/1.92 set(auto).
% 1.72/1.92 dependent: set(auto1).
% 1.72/1.92 dependent: set(process_input).
% 1.72/1.92 dependent: clear(print_kept).
% 1.72/1.92 dependent: clear(print_new_demod).
% 1.72/1.92 dependent: clear(print_back_demod).
% 1.72/1.92 dependent: clear(print_back_sub).
% 1.72/1.92 dependent: set(control_memory).
% 1.72/1.92 dependent: assign(max_mem, 12000).
% 1.72/1.92 dependent: assign(pick_given_ratio, 4).
% 1.72/1.92 dependent: assign(stats_level, 1).
% 1.72/1.92 dependent: assign(max_seconds, 10800).
% 1.72/1.92 clear(print_given).
% 1.72/1.92
% 1.72/1.92 list(usable).
% 1.72/1.92 0 [] A=A.
% 1.72/1.92 0 [] f(X,f(Y,Z))=f(f(X,Y),Z).
% 1.72/1.92 0 [] c(X)|d(X).
% 1.72/1.92 0 [] -c(X)| -d(X).
% 1.72/1.92 0 [] c(a1).
% 1.72/1.92 0 [] d(a2).
% 1.72/1.92 0 [] d(f(X,Y))| -c(X)| -c(Y).
% 1.72/1.92 0 [] c(f(X,Y))| -d(X)| -d(Y).
% 1.72/1.92 end_of_list.
% 1.72/1.92
% 1.72/1.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.72/1.92
% 1.72/1.92 This ia a non-Horn set with equality. The strategy will be
% 1.72/1.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.72/1.92 deletion, with positive clauses in sos and nonpositive
% 1.72/1.92 clauses in usable.
% 1.72/1.92
% 1.72/1.92 dependent: set(knuth_bendix).
% 1.72/1.92 dependent: set(anl_eq).
% 1.72/1.92 dependent: set(para_from).
% 1.72/1.92 dependent: set(para_into).
% 1.72/1.92 dependent: clear(para_from_right).
% 1.72/1.92 dependent: clear(para_into_right).
% 1.72/1.92 dependent: set(para_from_vars).
% 1.72/1.92 dependent: set(eq_units_both_ways).
% 1.72/1.92 dependent: set(dynamic_demod_all).
% 1.72/1.92 dependent: set(dynamic_demod).
% 1.72/1.92 dependent: set(order_eq).
% 1.72/1.92 dependent: set(back_demod).
% 1.72/1.92 dependent: set(lrpo).
% 1.72/1.92 dependent: set(hyper_res).
% 1.72/1.92 dependent: set(unit_deletion).
% 1.72/1.92 dependent: set(factor).
% 1.72/1.92
% 1.72/1.92 ------------> process usable:
% 1.72/1.92 ** KEPT (pick-wt=4): 1 [] -c(A)| -d(A).
% 1.72/1.92 ** KEPT (pick-wt=8): 2 [] d(f(A,B))| -c(A)| -c(B).
% 1.72/1.92 ** KEPT (pick-wt=8): 3 [] c(f(A,B))| -d(A)| -d(B).
% 1.72/1.92
% 1.72/1.92 ------------> process sos:
% 1.72/1.92 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.72/1.92 ** KEPT (pick-wt=11): 8 [copy,7,flip.1] f(f(A,B),C)=f(A,f(B,C)).
% 1.72/1.92 ---> New Demodulator: 9 [new_demod,8] f(f(A,B),C)=f(A,f(B,C)).
% 1.72/1.92 ** KEPT (pick-wt=4): 10 [] c(A)|d(A).
% 1.72/1.92 ** KEPT (pick-wt=2): 11 [] c(a1).
% 1.72/1.92 ** KEPT (pick-wt=2): 12 [] d(a2).
% 1.72/1.92 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.72/1.92 >>>> Starting back demodulation with 9.
% 1.72/1.92
% 1.72/1.92 ======= end of input processing =======
% 1.72/1.92
% 1.72/1.92 =========== start of search ===========
% 1.72/1.92
% 1.72/1.92 -------- PROOF --------
% 1.72/1.92
% 1.72/1.92 -----> EMPTY CLAUSE at 0.07 sec ----> 428 [hyper,403,1,20] $F.
% 1.72/1.92
% 1.72/1.92 Length of proof is 10. Level of proof is 5.
% 1.72/1.92
% 1.72/1.92 ---------------- PROOF ----------------
% 1.72/1.92 % SZS status Unsatisfiable
% 1.72/1.92 % SZS output start Refutation
% See solution above
% 1.72/1.92 ------------ end of proof -------------
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Search stopped by max_proofs option.
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Search stopped by max_proofs option.
% 1.72/1.92
% 1.72/1.92 ============ end of search ============
% 1.72/1.92
% 1.72/1.92 -------------- statistics -------------
% 1.72/1.92 clauses given 19
% 1.72/1.92 clauses generated 642
% 1.72/1.92 clauses kept 425
% 1.72/1.92 clauses forward subsumed 225
% 1.72/1.92 clauses back subsumed 1
% 1.72/1.92 Kbytes malloced 976
% 1.72/1.92
% 1.72/1.92 ----------- times (seconds) -----------
% 1.72/1.92 user CPU time 0.07 (0 hr, 0 min, 0 sec)
% 1.72/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.72/1.92
% 1.72/1.92 That finishes the proof of the theorem.
% 1.72/1.92
% 1.72/1.92 Process 31001 finished Wed Jul 27 03:02:34 2022
% 1.72/1.92 Otter interrupted
% 1.72/1.92 PROOF FOUND
%------------------------------------------------------------------------------