TSTP Solution File: LAT035-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 13:01:50 EDT 2022
% Result : Unsatisfiable 1.85s 2.07s
% Output : Refutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 8 ( 6 unt; 0 nHn; 5 RR)
% Number of literals : 10 ( 9 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( f(k(join(aa,bb))) != join(f(k(aa)),f(k(bb)))
| f(k(n0)) != n0 ),
file('LAT035-1.p',unknown),
[] ).
cnf(3,axiom,
A = A,
file('LAT035-1.p',unknown),
[] ).
cnf(27,axiom,
k(join(A,B)) = meet(k(A),k(B)),
file('LAT035-1.p',unknown),
[] ).
cnf(31,axiom,
k(n0) = n1,
file('LAT035-1.p',unknown),
[] ).
cnf(35,axiom,
f(meet(A,B)) = join(f(A),f(B)),
file('LAT035-1.p',unknown),
[] ).
cnf(37,axiom,
f(n1) = n0,
file('LAT035-1.p',unknown),
[] ).
cnf(38,plain,
( join(f(k(aa)),f(k(bb))) != join(f(k(aa)),f(k(bb)))
| n0 != n0 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),27,35,31,37]),
[iquote('back_demod,2,demod,27,35,31,37')] ).
cnf(274,plain,
$false,
inference(hyper,[status(thm)],[38,3,3]),
[iquote('hyper,38,3,3')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n026.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 08:40:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.85/2.06 ----- Otter 3.3f, August 2004 -----
% 1.85/2.06 The process was started by sandbox2 on n026.cluster.edu,
% 1.85/2.06 Wed Jul 27 08:40:09 2022
% 1.85/2.06 The command was "./otter". The process ID is 14197.
% 1.85/2.06
% 1.85/2.06 set(prolog_style_variables).
% 1.85/2.06 set(auto).
% 1.85/2.06 dependent: set(auto1).
% 1.85/2.06 dependent: set(process_input).
% 1.85/2.06 dependent: clear(print_kept).
% 1.85/2.06 dependent: clear(print_new_demod).
% 1.85/2.06 dependent: clear(print_back_demod).
% 1.85/2.06 dependent: clear(print_back_sub).
% 1.85/2.06 dependent: set(control_memory).
% 1.85/2.06 dependent: assign(max_mem, 12000).
% 1.85/2.06 dependent: assign(pick_given_ratio, 4).
% 1.85/2.06 dependent: assign(stats_level, 1).
% 1.85/2.06 dependent: assign(max_seconds, 10800).
% 1.85/2.06 clear(print_given).
% 1.85/2.06
% 1.85/2.06 list(usable).
% 1.85/2.06 0 [] A=A.
% 1.85/2.06 0 [] meet(X,X)=X.
% 1.85/2.06 0 [] join(X,X)=X.
% 1.85/2.06 0 [] meet(X,join(X,Y))=X.
% 1.85/2.06 0 [] join(X,meet(X,Y))=X.
% 1.85/2.06 0 [] meet(X,Y)=meet(Y,X).
% 1.85/2.06 0 [] join(X,Y)=join(Y,X).
% 1.85/2.06 0 [] meet(meet(X,Y),Z)=meet(X,meet(Y,Z)).
% 1.85/2.06 0 [] join(join(X,Y),Z)=join(X,join(Y,Z)).
% 1.85/2.06 0 [] meet(X,n0)=n0.
% 1.85/2.06 0 [] join(X,n0)=X.
% 1.85/2.06 0 [] meet(X,n1)=X.
% 1.85/2.06 0 [] join(X,n1)=n1.
% 1.85/2.06 0 [] meet(X,Z)!=X|meet(Z,join(X,Y))=join(X,meet(Y,Z)).
% 1.85/2.06 0 [] k(join(U,V))=meet(k(U),k(V)).
% 1.85/2.06 0 [] k(meet(U,V))=join(k(U),k(V)).
% 1.85/2.06 0 [] k(n0)=n1.
% 1.85/2.06 0 [] k(n1)=n0.
% 1.85/2.06 0 [] f(meet(U,V))=join(f(U),f(V)).
% 1.85/2.06 0 [] f(n1)=n0.
% 1.85/2.06 0 [] f(k(join(aa,bb)))!=join(f(k(aa)),f(k(bb)))|f(k(n0))!=n0.
% 1.85/2.06 end_of_list.
% 1.85/2.06
% 1.85/2.06 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.85/2.06
% 1.85/2.06 This is a Horn set with equality. The strategy will be
% 1.85/2.06 Knuth-Bendix and hyper_res, with positive clauses in
% 1.85/2.06 sos and nonpositive clauses in usable.
% 1.85/2.06
% 1.85/2.06 dependent: set(knuth_bendix).
% 1.85/2.06 dependent: set(anl_eq).
% 1.85/2.06 dependent: set(para_from).
% 1.85/2.06 dependent: set(para_into).
% 1.85/2.06 dependent: clear(para_from_right).
% 1.85/2.06 dependent: clear(para_into_right).
% 1.85/2.06 dependent: set(para_from_vars).
% 1.85/2.06 dependent: set(eq_units_both_ways).
% 1.85/2.06 dependent: set(dynamic_demod_all).
% 1.85/2.06 dependent: set(dynamic_demod).
% 1.85/2.06 dependent: set(order_eq).
% 1.85/2.06 dependent: set(back_demod).
% 1.85/2.06 dependent: set(lrpo).
% 1.85/2.06 dependent: set(hyper_res).
% 1.85/2.06 dependent: clear(order_hyper).
% 1.85/2.06
% 1.85/2.06 ------------> process usable:
% 1.85/2.06 ** KEPT (pick-wt=16): 1 [] meet(A,B)!=A|meet(B,join(A,C))=join(A,meet(C,B)).
% 1.85/2.06 ** KEPT (pick-wt=18): 2 [] f(k(join(aa,bb)))!=join(f(k(aa)),f(k(bb)))|f(k(n0))!=n0.
% 1.85/2.06
% 1.85/2.06 ------------> process sos:
% 1.85/2.06 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.85/2.06 ** KEPT (pick-wt=5): 4 [] meet(A,A)=A.
% 1.85/2.06 ---> New Demodulator: 5 [new_demod,4] meet(A,A)=A.
% 1.85/2.06 ** KEPT (pick-wt=5): 6 [] join(A,A)=A.
% 1.85/2.06 ---> New Demodulator: 7 [new_demod,6] join(A,A)=A.
% 1.85/2.06 ** KEPT (pick-wt=7): 8 [] meet(A,join(A,B))=A.
% 1.85/2.06 ---> New Demodulator: 9 [new_demod,8] meet(A,join(A,B))=A.
% 1.85/2.06 ** KEPT (pick-wt=7): 10 [] join(A,meet(A,B))=A.
% 1.85/2.06 ---> New Demodulator: 11 [new_demod,10] join(A,meet(A,B))=A.
% 1.85/2.06 ** KEPT (pick-wt=7): 12 [] meet(A,B)=meet(B,A).
% 1.85/2.06 ** KEPT (pick-wt=7): 13 [] join(A,B)=join(B,A).
% 1.85/2.06 ** KEPT (pick-wt=11): 14 [] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 1.85/2.06 ---> New Demodulator: 15 [new_demod,14] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 1.85/2.06 ** KEPT (pick-wt=11): 16 [] join(join(A,B),C)=join(A,join(B,C)).
% 1.85/2.06 ---> New Demodulator: 17 [new_demod,16] join(join(A,B),C)=join(A,join(B,C)).
% 1.85/2.06 ** KEPT (pick-wt=5): 18 [] meet(A,n0)=n0.
% 1.85/2.06 ---> New Demodulator: 19 [new_demod,18] meet(A,n0)=n0.
% 1.85/2.06 ** KEPT (pick-wt=5): 20 [] join(A,n0)=A.
% 1.85/2.06 ---> New Demodulator: 21 [new_demod,20] join(A,n0)=A.
% 1.85/2.06 ** KEPT (pick-wt=5): 22 [] meet(A,n1)=A.
% 1.85/2.06 ---> New Demodulator: 23 [new_demod,22] meet(A,n1)=A.
% 1.85/2.06 ** KEPT (pick-wt=5): 24 [] join(A,n1)=n1.
% 1.85/2.06 ---> New Demodulator: 25 [new_demod,24] join(A,n1)=n1.
% 1.85/2.06 ** KEPT (pick-wt=10): 26 [] k(join(A,B))=meet(k(A),k(B)).
% 1.85/2.06 ---> New Demodulator: 27 [new_demod,26] k(join(A,B))=meet(k(A),k(B)).
% 1.85/2.06 ** KEPT (pick-wt=10): 28 [] k(meet(A,B))=join(k(A),k(B)).
% 1.85/2.06 ---> New Demodulator: 29 [new_demod,28] k(meet(A,B))=join(k(A),k(B)).
% 1.85/2.06 ** KEPT (pick-wt=4): 30 [] k(n0)=n1.
% 1.85/2.06 ---> New Demodulator: 31 [new_demod,30] k(n0)=n1.
% 1.85/2.06 ** KEPT (pick-wt=4): 32 [] k(n1)=n0.
% 1.85/2.06 ---> New Demodulator: 33 [new_demod,32] k(n1)=n0.
% 1.85/2.06 ** KEPT (pick-wt=10): 34 [] f(meet(A,B))=join(f(A),f(B)).
% 1.85/2.06 ---> New Demodulator: 35 [new_demod,34] f(meet(A,B))=join(f(A),f(B)).
% 1.85/2.06 ** KEPT (pick-wt=4): 36 [] f(n1)=n0.
% 1.85/2.06 ---> New Demodulator: 37 [new_demod,36] f(n1)=n0.
% 1.85/2.06 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.85/2.06 >>>> Starting back demodulation with 5.
% 1.85/2.07 >>>> Starting back demodulation with 7.
% 1.85/2.07 >>>> Starting back demodulation with 9.
% 1.85/2.07 >>>> Starting back demodulation with 11.
% 1.85/2.07 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] meet(A,B)=meet(B,A).
% 1.85/2.07 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] join(A,B)=join(B,A).
% 1.85/2.07 >>>> Starting back demodulation with 15.
% 1.85/2.07 >>>> Starting back demodulation with 17.
% 1.85/2.07 >>>> Starting back demodulation with 19.
% 1.85/2.07 >>>> Starting back demodulation with 21.
% 1.85/2.07 >>>> Starting back demodulation with 23.
% 1.85/2.07 >>>> Starting back demodulation with 25.
% 1.85/2.07 >>>> Starting back demodulation with 27.
% 1.85/2.07 >> back demodulating 2 with 27.
% 1.85/2.07 >>>> Starting back demodulation with 29.
% 1.85/2.07 >>>> Starting back demodulation with 31.
% 1.85/2.07 >>>> Starting back demodulation with 33.
% 1.85/2.07 >>>> Starting back demodulation with 35.
% 1.85/2.07 >>>> Starting back demodulation with 37.
% 1.85/2.07
% 1.85/2.07 ======= end of input processing =======
% 1.85/2.07
% 1.85/2.07 =========== start of search ===========
% 1.85/2.07
% 1.85/2.07 -------- PROOF --------
% 1.85/2.07
% 1.85/2.07 -----> EMPTY CLAUSE at 0.01 sec ----> 274 [hyper,38,3,3] $F.
% 1.85/2.07
% 1.85/2.07 Length of proof is 1. Level of proof is 1.
% 1.85/2.07
% 1.85/2.07 ---------------- PROOF ----------------
% 1.85/2.07 % SZS status Unsatisfiable
% 1.85/2.07 % SZS output start Refutation
% See solution above
% 1.85/2.07 ------------ end of proof -------------
% 1.85/2.07
% 1.85/2.07
% 1.85/2.07 Search stopped by max_proofs option.
% 1.85/2.07
% 1.85/2.07
% 1.85/2.07 Search stopped by max_proofs option.
% 1.85/2.07
% 1.85/2.07 ============ end of search ============
% 1.85/2.07
% 1.85/2.07 -------------- statistics -------------
% 1.85/2.07 clauses given 46
% 1.85/2.07 clauses generated 1205
% 1.85/2.07 clauses kept 215
% 1.85/2.07 clauses forward subsumed 943
% 1.85/2.07 clauses back subsumed 12
% 1.85/2.07 Kbytes malloced 1953
% 1.85/2.07
% 1.85/2.07 ----------- times (seconds) -----------
% 1.85/2.07 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.85/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.85/2.07 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.85/2.07
% 1.85/2.07 That finishes the proof of the theorem.
% 1.85/2.07
% 1.85/2.07 Process 14197 finished Wed Jul 27 08:40:11 2022
% 1.85/2.07 Otter interrupted
% 1.85/2.07 PROOF FOUND
%------------------------------------------------------------------------------