TSTP Solution File: LAT239-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT239-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:02:10 EDT 2022
% Result : Unsatisfiable 2.32s 2.57s
% Output : Refutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 36 ( 34 unt; 0 nHn; 13 RR)
% Number of literals : 40 ( 39 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( meet(A,B) != zero
| join(A,B) != one
| complement(A) = B ),
file('LAT239-1.p',unknown),
[] ).
cnf(2,axiom,
join(complement(b),complement(a)) != complement(a),
file('LAT239-1.p',unknown),
[] ).
cnf(3,axiom,
A = A,
file('LAT239-1.p',unknown),
[] ).
cnf(8,axiom,
meet(A,join(A,B)) = A,
file('LAT239-1.p',unknown),
[] ).
cnf(10,axiom,
join(A,meet(A,B)) = A,
file('LAT239-1.p',unknown),
[] ).
cnf(12,axiom,
meet(A,B) = meet(B,A),
file('LAT239-1.p',unknown),
[] ).
cnf(13,axiom,
join(A,B) = join(B,A),
file('LAT239-1.p',unknown),
[] ).
cnf(14,axiom,
meet(meet(A,B),C) = meet(A,meet(B,C)),
file('LAT239-1.p',unknown),
[] ).
cnf(16,axiom,
join(join(A,B),C) = join(A,join(B,C)),
file('LAT239-1.p',unknown),
[] ).
cnf(18,axiom,
join(A,complement(A)) = one,
file('LAT239-1.p',unknown),
[] ).
cnf(21,axiom,
meet(A,complement(A)) = zero,
file('LAT239-1.p',unknown),
[] ).
cnf(22,axiom,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,join(meet(A,C),meet(C,join(B,D))))),
file('LAT239-1.p',unknown),
[] ).
cnf(23,axiom,
meet(b,a) = a,
file('LAT239-1.p',unknown),
[] ).
cnf(25,plain,
meet(A,join(B,join(meet(A,C),meet(C,join(B,D))))) = meet(A,join(B,meet(C,join(A,D)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[22])]),
[iquote('copy,22,flip.1')] ).
cnf(29,plain,
meet(A,one) = A,
inference(para_into,[status(thm),theory(equality)],[8,18]),
[iquote('para_into,8.1.1.2,18.1.1')] ).
cnf(32,plain,
join(b,a) = b,
inference(para_into,[status(thm),theory(equality)],[10,23]),
[iquote('para_into,10.1.1.2,23.1.1')] ).
cnf(35,plain,
join(A,zero) = A,
inference(para_into,[status(thm),theory(equality)],[10,21]),
[iquote('para_into,10.1.1.2,20.1.1')] ).
cnf(38,plain,
meet(one,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,29])]),
[iquote('para_into,12.1.1,28.1.1,flip.1')] ).
cnf(43,plain,
meet(complement(A),A) = zero,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,21])]),
[iquote('para_into,12.1.1,20.1.1,flip.1')] ).
cnf(53,plain,
join(one,A) = one,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[38,8])]),
[iquote('para_into,38.1.1,8.1.1,flip.1')] ).
cnf(57,plain,
join(zero,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,35])]),
[iquote('para_into,13.1.1,34.1.1,flip.1')] ).
cnf(59,plain,
join(a,b) = b,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,32])]),
[iquote('para_into,13.1.1,32.1.1,flip.1')] ).
cnf(60,plain,
join(complement(A),A) = one,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,18])]),
[iquote('para_into,13.1.1,18.1.1,flip.1')] ).
cnf(65,plain,
join(complement(a),complement(b)) != complement(a),
inference(para_from,[status(thm),theory(equality)],[13,2]),
[iquote('para_from,13.1.1,2.1.1')] ).
cnf(75,plain,
meet(zero,A) = zero,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[57,10])]),
[iquote('para_into,56.1.1,10.1.1,flip.1')] ).
cnf(104,plain,
meet(complement(A),meet(A,B)) = zero,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[43,14]),75])]),
[iquote('para_from,42.1.1,14.1.1.1,demod,75,flip.1')] ).
cnf(111,plain,
join(A,join(complement(A),B)) = one,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,18]),53])]),
[iquote('para_into,16.1.1.1,18.1.1,demod,53,flip.1')] ).
cnf(133,plain,
join(complement(A),join(A,B)) = one,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[60,16]),53])]),
[iquote('para_from,60.1.1,16.1.1.1,demod,53,flip.1')] ).
cnf(332,plain,
meet(complement(b),a) = zero,
inference(para_into,[status(thm),theory(equality)],[104,23]),
[iquote('para_into,104.1.1.2,23.1.1')] ).
cnf(340,plain,
meet(a,complement(b)) = zero,
inference(para_into,[status(thm),theory(equality)],[332,12]),
[iquote('para_into,332.1.1,12.1.1')] ).
cnf(357,plain,
meet(a,join(A,meet(complement(b),join(A,B)))) = meet(a,join(A,meet(complement(b),join(a,B)))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[340,25]),57]),
[iquote('para_from,340.1.1,25.1.1.2.2.1,demod,57')] ).
cnf(374,plain,
( meet(A,join(complement(A),B)) != zero
| one != one
| join(complement(A),B) = complement(A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[111,1])]),
[iquote('para_from,111.1.1,1.2.1,flip.3')] ).
cnf(380,plain,
join(complement(a),b) = one,
inference(para_into,[status(thm),theory(equality)],[133,59]),
[iquote('para_into,133.1.1.2,58.1.1')] ).
cnf(681,plain,
meet(a,join(complement(a),complement(b))) = zero,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[357,380]),29,59,43,35,21]),
[iquote('para_into,357.1.1.2.2.2,380.1.1,demod,29,59,43,35,21')] ).
cnf(685,plain,
join(complement(a),complement(b)) = complement(a),
inference(hyper,[status(thm)],[681,374,3]),
[iquote('hyper,681,374,3')] ).
cnf(687,plain,
$false,
inference(binary,[status(thm)],[685,65]),
[iquote('binary,685.1,65.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT239-1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 08:18:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.65/1.87 ----- Otter 3.3f, August 2004 -----
% 1.65/1.87 The process was started by sandbox on n019.cluster.edu,
% 1.65/1.87 Wed Jul 27 08:18:22 2022
% 1.65/1.87 The command was "./otter". The process ID is 3234.
% 1.65/1.87
% 1.65/1.87 set(prolog_style_variables).
% 1.65/1.87 set(auto).
% 1.65/1.87 dependent: set(auto1).
% 1.65/1.87 dependent: set(process_input).
% 1.65/1.87 dependent: clear(print_kept).
% 1.65/1.87 dependent: clear(print_new_demod).
% 1.65/1.87 dependent: clear(print_back_demod).
% 1.65/1.87 dependent: clear(print_back_sub).
% 1.65/1.87 dependent: set(control_memory).
% 1.65/1.87 dependent: assign(max_mem, 12000).
% 1.65/1.87 dependent: assign(pick_given_ratio, 4).
% 1.65/1.87 dependent: assign(stats_level, 1).
% 1.65/1.87 dependent: assign(max_seconds, 10800).
% 1.65/1.87 clear(print_given).
% 1.65/1.87
% 1.65/1.87 list(usable).
% 1.65/1.87 0 [] A=A.
% 1.65/1.87 0 [] meet(X,X)=X.
% 1.65/1.87 0 [] join(X,X)=X.
% 1.65/1.87 0 [] meet(X,join(X,Y))=X.
% 1.65/1.87 0 [] join(X,meet(X,Y))=X.
% 1.65/1.87 0 [] meet(X,Y)=meet(Y,X).
% 1.65/1.87 0 [] join(X,Y)=join(Y,X).
% 1.65/1.87 0 [] meet(meet(X,Y),Z)=meet(X,meet(Y,Z)).
% 1.65/1.87 0 [] join(join(X,Y),Z)=join(X,join(Y,Z)).
% 1.65/1.87 0 [] join(X,complement(X))=one.
% 1.65/1.87 0 [] meet(X,complement(X))=zero.
% 1.65/1.87 0 [] meet(X,Y)!=zero|join(X,Y)!=one|complement(X)=Y.
% 1.65/1.87 0 [] meet(X,join(Y,meet(Z,join(X,U))))=meet(X,join(Y,join(meet(X,Z),meet(Z,join(Y,U))))).
% 1.65/1.87 0 [] meet(b,a)=a.
% 1.65/1.87 0 [] join(complement(b),complement(a))!=complement(a).
% 1.65/1.87 end_of_list.
% 1.65/1.87
% 1.65/1.87 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.65/1.87
% 1.65/1.87 This is a Horn set with equality. The strategy will be
% 1.65/1.87 Knuth-Bendix and hyper_res, with positive clauses in
% 1.65/1.87 sos and nonpositive clauses in usable.
% 1.65/1.87
% 1.65/1.87 dependent: set(knuth_bendix).
% 1.65/1.87 dependent: set(anl_eq).
% 1.65/1.87 dependent: set(para_from).
% 1.65/1.87 dependent: set(para_into).
% 1.65/1.87 dependent: clear(para_from_right).
% 1.65/1.87 dependent: clear(para_into_right).
% 1.65/1.87 dependent: set(para_from_vars).
% 1.65/1.87 dependent: set(eq_units_both_ways).
% 1.65/1.87 dependent: set(dynamic_demod_all).
% 1.65/1.87 dependent: set(dynamic_demod).
% 1.65/1.87 dependent: set(order_eq).
% 1.65/1.87 dependent: set(back_demod).
% 1.65/1.87 dependent: set(lrpo).
% 1.65/1.87 dependent: set(hyper_res).
% 1.65/1.87 dependent: clear(order_hyper).
% 1.65/1.87
% 1.65/1.87 ------------> process usable:
% 1.65/1.87 ** KEPT (pick-wt=14): 1 [] meet(A,B)!=zero|join(A,B)!=one|complement(A)=B.
% 1.65/1.87 ** KEPT (pick-wt=8): 2 [] join(complement(b),complement(a))!=complement(a).
% 1.65/1.87
% 1.65/1.87 ------------> process sos:
% 1.65/1.87 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.65/1.87 ** KEPT (pick-wt=5): 4 [] meet(A,A)=A.
% 1.65/1.87 ---> New Demodulator: 5 [new_demod,4] meet(A,A)=A.
% 1.65/1.87 ** KEPT (pick-wt=5): 6 [] join(A,A)=A.
% 1.65/1.87 ---> New Demodulator: 7 [new_demod,6] join(A,A)=A.
% 1.65/1.87 ** KEPT (pick-wt=7): 8 [] meet(A,join(A,B))=A.
% 1.65/1.87 ---> New Demodulator: 9 [new_demod,8] meet(A,join(A,B))=A.
% 1.65/1.87 ** KEPT (pick-wt=7): 10 [] join(A,meet(A,B))=A.
% 1.65/1.87 ---> New Demodulator: 11 [new_demod,10] join(A,meet(A,B))=A.
% 1.65/1.87 ** KEPT (pick-wt=7): 12 [] meet(A,B)=meet(B,A).
% 1.65/1.87 ** KEPT (pick-wt=7): 13 [] join(A,B)=join(B,A).
% 1.65/1.87 ** KEPT (pick-wt=11): 14 [] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 1.65/1.87 ---> New Demodulator: 15 [new_demod,14] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 1.65/1.87 ** KEPT (pick-wt=11): 16 [] join(join(A,B),C)=join(A,join(B,C)).
% 1.65/1.87 ---> New Demodulator: 17 [new_demod,16] join(join(A,B),C)=join(A,join(B,C)).
% 1.65/1.87 ** KEPT (pick-wt=6): 18 [] join(A,complement(A))=one.
% 1.65/1.87 ---> New Demodulator: 19 [new_demod,18] join(A,complement(A))=one.
% 1.65/1.87 ** KEPT (pick-wt=6): 20 [] meet(A,complement(A))=zero.
% 1.65/1.87 ---> New Demodulator: 21 [new_demod,20] meet(A,complement(A))=zero.
% 1.65/1.87 ** KEPT (pick-wt=23): 22 [] meet(A,join(B,meet(C,join(A,D))))=meet(A,join(B,join(meet(A,C),meet(C,join(B,D))))).
% 1.65/1.87 ** KEPT (pick-wt=5): 23 [] meet(b,a)=a.
% 1.65/1.87 ---> New Demodulator: 24 [new_demod,23] meet(b,a)=a.
% 1.65/1.87 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.65/1.87 >>>> Starting back demodulation with 5.
% 1.65/1.87 >>>> Starting back demodulation with 7.
% 1.65/1.87 >>>> Starting back demodulation with 9.
% 1.65/1.87 >>>> Starting back demodulation with 11.
% 1.65/1.87 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] meet(A,B)=meet(B,A).
% 1.65/1.87 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] join(A,B)=join(B,A).
% 1.65/1.87 >>>> Starting back demodulation with 15.
% 1.65/1.87 >>>> Starting back demodulation with 17.
% 1.65/1.87 >>>> Starting back demodulation with 19.
% 1.65/1.87 >>>> Starting back demodulation with 21.
% 1.65/1.87 ** KEPT (pick-wt=23): 25 [copy,22,flip.1] meet(A,join(B,join(meet(A,C),meet(C,join(B,D)))))=meet(A,join(B,meet(C,join(A,D)))).
% 1.65/1.87 >>>> Starting back demodulation with 24.
% 2.32/2.57 Following clause subsumed by 22 during input processing: 0 [copy,25,flip.1] meet(A,join(B,meet(C,join(A,D))))=meet(A,join(B,join(meet(A,C),meet(C,join(B,D))))).
% 2.32/2.57
% 2.32/2.57 ======= end of input processing =======
% 2.32/2.57
% 2.32/2.57 =========== start of search ===========
% 2.32/2.57
% 2.32/2.57
% 2.32/2.57 Resetting weight limit to 9.
% 2.32/2.57
% 2.32/2.57
% 2.32/2.57 Resetting weight limit to 9.
% 2.32/2.57
% 2.32/2.57 sos_size=350
% 2.32/2.57
% 2.32/2.57 -------- PROOF --------
% 2.32/2.57
% 2.32/2.57 ----> UNIT CONFLICT at 0.70 sec ----> 687 [binary,685.1,65.1] $F.
% 2.32/2.57
% 2.32/2.57 Length of proof is 22. Level of proof is 9.
% 2.32/2.57
% 2.32/2.57 ---------------- PROOF ----------------
% 2.32/2.57 % SZS status Unsatisfiable
% 2.32/2.57 % SZS output start Refutation
% See solution above
% 2.32/2.57 ------------ end of proof -------------
% 2.32/2.57
% 2.32/2.57
% 2.32/2.57 Search stopped by max_proofs option.
% 2.32/2.57
% 2.32/2.57
% 2.32/2.57 Search stopped by max_proofs option.
% 2.32/2.57
% 2.32/2.57 ============ end of search ============
% 2.32/2.57
% 2.32/2.57 -------------- statistics -------------
% 2.32/2.57 clauses given 350
% 2.32/2.57 clauses generated 115589
% 2.32/2.57 clauses kept 487
% 2.32/2.57 clauses forward subsumed 29168
% 2.32/2.57 clauses back subsumed 24
% 2.32/2.57 Kbytes malloced 6835
% 2.32/2.57
% 2.32/2.57 ----------- times (seconds) -----------
% 2.32/2.57 user CPU time 0.70 (0 hr, 0 min, 0 sec)
% 2.32/2.57 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.32/2.57 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.32/2.57
% 2.32/2.57 That finishes the proof of the theorem.
% 2.32/2.57
% 2.32/2.57 Process 3234 finished Wed Jul 27 08:18:24 2022
% 2.32/2.57 Otter interrupted
% 2.32/2.57 PROOF FOUND
%------------------------------------------------------------------------------