TSTP Solution File: LAT019-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT019-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 13:01:47 EDT 2022
% Result : Unsatisfiable 2.12s 2.33s
% Output : Refutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 7 RR)
% Number of literals : 47 ( 46 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('LAT019-1.p',unknown),
[] ).
cnf(2,plain,
meet(join(a,b),join(a,c)) != join(a,meet(b,c)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(5,axiom,
meet(A,A) = A,
file('LAT019-1.p',unknown),
[] ).
cnf(7,axiom,
join(A,A) = A,
file('LAT019-1.p',unknown),
[] ).
cnf(8,axiom,
meet(A,B) = meet(B,A),
file('LAT019-1.p',unknown),
[] ).
cnf(9,axiom,
join(A,B) = join(B,A),
file('LAT019-1.p',unknown),
[] ).
cnf(11,axiom,
meet(meet(A,B),C) = meet(A,meet(B,C)),
file('LAT019-1.p',unknown),
[] ).
cnf(13,axiom,
join(join(A,B),C) = join(A,join(B,C)),
file('LAT019-1.p',unknown),
[] ).
cnf(16,axiom,
meet(join(A,meet(B,C)),join(A,B)) = join(A,meet(B,C)),
file('LAT019-1.p',unknown),
[] ).
cnf(19,axiom,
meet(A,join(B,C)) = join(meet(A,B),meet(A,C)),
file('LAT019-1.p',unknown),
[] ).
cnf(20,plain,
join(meet(join(A,meet(B,C)),A),meet(join(A,meet(B,C)),B)) = join(A,meet(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),19]),
[iquote('back_demod,16,demod,19')] ).
cnf(24,plain,
join(meet(join(a,b),a),meet(join(a,b),c)) != join(a,meet(b,c)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),19]),
[iquote('back_demod,2,demod,19')] ).
cnf(27,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,5])]),
[iquote('para_into,10.1.1.1,4.1.1,flip.1')] ).
cnf(35,plain,
meet(A,meet(B,A)) = meet(A,B),
inference(para_into,[status(thm),theory(equality)],[27,8]),
[iquote('para_into,26.1.1.2,8.1.1')] ).
cnf(40,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,9]),13]),
[iquote('para_into,12.1.1.1,9.1.1,demod,13')] ).
cnf(41,plain,
join(A,join(A,B)) = join(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,7])]),
[iquote('para_into,12.1.1.1,6.1.1,flip.1')] ).
cnf(43,plain,
join(A,join(B,C)) = join(B,join(C,A)),
inference(para_into,[status(thm),theory(equality)],[13,9]),
[iquote('para_into,12.1.1,9.1.1')] ).
cnf(50,plain,
join(A,join(B,A)) = join(A,B),
inference(para_into,[status(thm),theory(equality)],[41,9]),
[iquote('para_into,41.1.1.2,9.1.1')] ).
cnf(51,plain,
meet(join(A,B),C) = join(meet(C,A),meet(C,B)),
inference(para_into,[status(thm),theory(equality)],[19,8]),
[iquote('para_into,18.1.1,8.1.1')] ).
cnf(54,plain,
join(meet(A,B),meet(A,C)) = meet(join(B,C),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[51])]),
[iquote('copy,51,flip.1')] ).
cnf(59,plain,
join(A,join(B,join(C,A))) = join(A,join(B,C)),
inference(para_into,[status(thm),theory(equality)],[50,13]),
[iquote('para_into,49.1.1.2,12.1.1')] ).
cnf(62,plain,
join(A,join(B,join(A,C))) = join(A,join(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[50,13]),13,13])]),
[iquote('para_from,49.1.1,12.1.1.1,demod,13,13,flip.1')] ).
cnf(129,plain,
join(meet(join(A,meet(B,C)),B),meet(join(A,meet(B,C)),A)) = join(A,meet(B,C)),
inference(para_into,[status(thm),theory(equality)],[20,9]),
[iquote('para_into,20.1.1,9.1.1')] ).
cnf(132,plain,
join(meet(join(A,meet(B,C)),B),join(A,meet(B,C))) = join(A,meet(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[20,50]),129]),
[iquote('para_from,20.1.1,49.1.1.2,demod,129')] ).
cnf(146,plain,
join(A,join(B,C)) = join(C,join(B,A)),
inference(para_into,[status(thm),theory(equality)],[43,9]),
[iquote('para_into,43.1.1.2,9.1.1')] ).
cnf(176,plain,
join(meet(join(a,b),a),join(meet(c,a),meet(c,b))) != join(a,meet(b,c)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,8]),19]),
[iquote('para_into,24.1.1.2,8.1.1,demod,19')] ).
cnf(247,plain,
join(meet(A,B),meet(B,C)) = meet(join(A,C),B),
inference(para_into,[status(thm),theory(equality)],[54,8]),
[iquote('para_into,54.1.1.1,8.1.1')] ).
cnf(249,plain,
meet(join(A,B),A) = join(A,meet(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[54,5])]),
[iquote('para_into,54.1.1.1,4.1.1,flip.1')] ).
cnf(262,plain,
meet(join(A,meet(B,C)),B) = join(meet(B,A),meet(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[54,27])]),
[iquote('para_into,54.1.1.2,26.1.1,flip.1')] ).
cnf(265,plain,
meet(join(A,B),B) = join(meet(B,A),B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[54,5])]),
[iquote('para_into,54.1.1.2,4.1.1,flip.1')] ).
cnf(299,plain,
join(a,join(meet(a,b),join(meet(c,a),meet(c,b)))) != join(a,meet(b,c)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[176]),249,13]),
[iquote('back_demod,176,demod,249,13')] ).
cnf(345,plain,
join(meet(A,B),join(meet(A,C),B)) = join(B,meet(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[132]),262,13,50]),
[iquote('back_demod,132,demod,262,13,50')] ).
cnf(399,plain,
join(A,join(meet(A,B),B)) = join(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[265,41]),5,249,13,62])]),
[iquote('para_into,265.1.1.1,41.1.1,demod,5,249,13,62,flip.1')] ).
cnf(572,plain,
join(meet(A,B),join(B,A)) = join(A,B),
inference(para_into,[status(thm),theory(equality)],[399,43]),
[iquote('para_into,399.1.1,43.1.1')] ).
cnf(812,plain,
meet(join(A,B),meet(A,B)) = meet(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[572,249]),19,11,5,11,35,7,7]),
[iquote('para_from,572.1.1,248.1.1.1,demod,19,11,5,11,35,7,7')] ).
cnf(868,plain,
meet(join(A,B),meet(B,A)) = meet(B,A),
inference(para_into,[status(thm),theory(equality)],[812,9]),
[iquote('para_into,812.1.1.1,9.1.1')] ).
cnf(1257,plain,
meet(join(A,B),C) = join(meet(A,C),meet(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[247,8])]),
[iquote('para_into,247.1.1.2,8.1.1,flip.1')] ).
cnf(1568,plain,
join(meet(A,B),meet(B,A)) = meet(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[868]),1257,35,27]),
[iquote('back_demod,868,demod,1257,35,27')] ).
cnf(1934,plain,
join(meet(A,B),join(C,meet(B,A))) = join(meet(A,B),C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1568,59]),50])]),
[iquote('para_from,1568.1.1,59.1.1.2.2,demod,50,flip.1')] ).
cnf(1935,plain,
join(A,meet(B,C)) = join(meet(B,C),join(meet(C,B),A)),
inference(para_from,[status(thm),theory(equality)],[1568,146]),
[iquote('para_from,1568.1.1,146.1.1.2')] ).
cnf(1938,plain,
join(A,meet(B,C)) = join(meet(C,B),A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1568,40]),1934]),
[iquote('para_from,1568.1.1,40.1.1.2,demod,1934')] ).
cnf(1940,plain,
join(meet(A,B),join(meet(B,A),C)) = join(meet(B,A),C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1568,13])]),
[iquote('para_from,1568.1.1,12.1.1.1,flip.1')] ).
cnf(1948,plain,
join(meet(A,B),C) = join(C,meet(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1935])]),1940]),
[iquote('copy,1935,flip.1,demod,1940')] ).
cnf(2119,plain,
join(A,join(meet(B,C),D)) = join(meet(C,B),join(D,A)),
inference(para_from,[status(thm),theory(equality)],[1938,146]),
[iquote('para_from,1938.1.1,146.1.1.2')] ).
cnf(3889,plain,
join(meet(A,B),join(B,meet(C,A))) = join(B,meet(A,C)),
inference(para_into,[status(thm),theory(equality)],[345,1948]),
[iquote('para_into,344.1.1.2,1948.1.1')] ).
cnf(3957,plain,
join(meet(b,a),join(a,meet(c,b))) != join(a,meet(b,c)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2119,299]),13,345]),
[iquote('para_from,2119.1.1,299.1.1,demod,13,345')] ).
cnf(3958,plain,
$false,
inference(binary,[status(thm)],[3957,3889]),
[iquote('binary,3957.1,3889.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT019-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n016.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 08:56:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.12/2.33 ----- Otter 3.3f, August 2004 -----
% 2.12/2.33 The process was started by sandbox2 on n016.cluster.edu,
% 2.12/2.33 Wed Jul 27 08:56:52 2022
% 2.12/2.33 The command was "./otter". The process ID is 19320.
% 2.12/2.33
% 2.12/2.33 set(prolog_style_variables).
% 2.12/2.33 set(auto).
% 2.12/2.33 dependent: set(auto1).
% 2.12/2.33 dependent: set(process_input).
% 2.12/2.33 dependent: clear(print_kept).
% 2.12/2.33 dependent: clear(print_new_demod).
% 2.12/2.33 dependent: clear(print_back_demod).
% 2.12/2.33 dependent: clear(print_back_sub).
% 2.12/2.33 dependent: set(control_memory).
% 2.12/2.33 dependent: assign(max_mem, 12000).
% 2.12/2.33 dependent: assign(pick_given_ratio, 4).
% 2.12/2.33 dependent: assign(stats_level, 1).
% 2.12/2.33 dependent: assign(max_seconds, 10800).
% 2.12/2.33 clear(print_given).
% 2.12/2.33
% 2.12/2.33 list(usable).
% 2.12/2.33 0 [] A=A.
% 2.12/2.33 0 [] meet(X,X)=X.
% 2.12/2.33 0 [] join(X,X)=X.
% 2.12/2.33 0 [] meet(X,Y)=meet(Y,X).
% 2.12/2.33 0 [] join(X,Y)=join(Y,X).
% 2.12/2.33 0 [] meet(meet(X,Y),Z)=meet(X,meet(Y,Z)).
% 2.12/2.33 0 [] join(join(X,Y),Z)=join(X,join(Y,Z)).
% 2.12/2.33 0 [] join(meet(X,join(Y,Z)),meet(X,Y))=meet(X,join(Y,Z)).
% 2.12/2.33 0 [] meet(join(X,meet(Y,Z)),join(X,Y))=join(X,meet(Y,Z)).
% 2.12/2.33 0 [] meet(X,join(Y,Z))=join(meet(X,Y),meet(X,Z)).
% 2.12/2.33 0 [] join(a,meet(b,c))!=meet(join(a,b),join(a,c)).
% 2.12/2.33 end_of_list.
% 2.12/2.33
% 2.12/2.33 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.12/2.33
% 2.12/2.33 All clauses are units, and equality is present; the
% 2.12/2.33 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.12/2.33
% 2.12/2.33 dependent: set(knuth_bendix).
% 2.12/2.33 dependent: set(anl_eq).
% 2.12/2.33 dependent: set(para_from).
% 2.12/2.33 dependent: set(para_into).
% 2.12/2.33 dependent: clear(para_from_right).
% 2.12/2.33 dependent: clear(para_into_right).
% 2.12/2.33 dependent: set(para_from_vars).
% 2.12/2.33 dependent: set(eq_units_both_ways).
% 2.12/2.33 dependent: set(dynamic_demod_all).
% 2.12/2.33 dependent: set(dynamic_demod).
% 2.12/2.33 dependent: set(order_eq).
% 2.12/2.33 dependent: set(back_demod).
% 2.12/2.33 dependent: set(lrpo).
% 2.12/2.33
% 2.12/2.33 ------------> process usable:
% 2.12/2.33 ** KEPT (pick-wt=13): 2 [copy,1,flip.1] meet(join(a,b),join(a,c))!=join(a,meet(b,c)).
% 2.12/2.33
% 2.12/2.33 ------------> process sos:
% 2.12/2.33 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.12/2.33 ** KEPT (pick-wt=5): 4 [] meet(A,A)=A.
% 2.12/2.33 ---> New Demodulator: 5 [new_demod,4] meet(A,A)=A.
% 2.12/2.33 ** KEPT (pick-wt=5): 6 [] join(A,A)=A.
% 2.12/2.33 ---> New Demodulator: 7 [new_demod,6] join(A,A)=A.
% 2.12/2.33 ** KEPT (pick-wt=7): 8 [] meet(A,B)=meet(B,A).
% 2.12/2.33 ** KEPT (pick-wt=7): 9 [] join(A,B)=join(B,A).
% 2.12/2.33 ** KEPT (pick-wt=11): 10 [] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 2.12/2.33 ---> New Demodulator: 11 [new_demod,10] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 2.12/2.33 ** KEPT (pick-wt=11): 12 [] join(join(A,B),C)=join(A,join(B,C)).
% 2.12/2.33 ---> New Demodulator: 13 [new_demod,12] join(join(A,B),C)=join(A,join(B,C)).
% 2.12/2.33 ** KEPT (pick-wt=15): 14 [] join(meet(A,join(B,C)),meet(A,B))=meet(A,join(B,C)).
% 2.12/2.33 ---> New Demodulator: 15 [new_demod,14] join(meet(A,join(B,C)),meet(A,B))=meet(A,join(B,C)).
% 2.12/2.33 ** KEPT (pick-wt=15): 16 [] meet(join(A,meet(B,C)),join(A,B))=join(A,meet(B,C)).
% 2.12/2.33 ---> New Demodulator: 17 [new_demod,16] meet(join(A,meet(B,C)),join(A,B))=join(A,meet(B,C)).
% 2.12/2.33 ** KEPT (pick-wt=13): 18 [] meet(A,join(B,C))=join(meet(A,B),meet(A,C)).
% 2.12/2.33 ---> New Demodulator: 19 [new_demod,18] meet(A,join(B,C))=join(meet(A,B),meet(A,C)).
% 2.12/2.33 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.12/2.33 >>>> Starting back demodulation with 5.
% 2.12/2.33 >>>> Starting back demodulation with 7.
% 2.12/2.33 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] meet(A,B)=meet(B,A).
% 2.12/2.33 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] join(A,B)=join(B,A).
% 2.12/2.33 >>>> Starting back demodulation with 11.
% 2.12/2.33 >>>> Starting back demodulation with 13.
% 2.12/2.33 >>>> Starting back demodulation with 15.
% 2.12/2.33 >>>> Starting back demodulation with 17.
% 2.12/2.33 >>>> Starting back demodulation with 19.
% 2.12/2.33 >> back demodulating 16 with 19.
% 2.12/2.33 >> back demodulating 14 with 19.
% 2.12/2.33 >> back demodulating 2 with 19.
% 2.12/2.33 >>>> Starting back demodulation with 21.
% 2.12/2.33 >>>> Starting back demodulation with 23.
% 2.12/2.33
% 2.12/2.33 ======= end of input processing =======
% 2.12/2.33
% 2.12/2.33 =========== start of search ===========
% 2.12/2.33
% 2.12/2.33
% 2.12/2.33 Resetting weight limit to 17.
% 2.12/2.33
% 2.12/2.33
% 2.12/2.33 Resetting weight limit to 17.
% 2.12/2.33
% 2.12/2.33 sos_size=2147
% 2.12/2.33
% 2.12/2.33 -------- PROOF --------
% 2.12/2.33
% 2.12/2.33 ----> UNIT CONFLICT at 0.45 sec ----> 3958 [binary,3957.1,3889.1] $F.
% 2.12/2.33
% 2.12/2.33 Length of proof is 37. Level of proof is 12.
% 2.12/2.33
% 2.12/2.33 ---------------- PROOF ----------------
% 2.12/2.33 % SZS status Unsatisfiable
% 2.12/2.33 % SZS output start Refutation
% See solution above
% 2.12/2.33 ------------ end of proof -------------
% 2.12/2.33
% 2.12/2.33
% 2.12/2.33 Search stopped by max_proofs option.
% 2.12/2.33
% 2.12/2.33
% 2.12/2.33 Search stopped by max_proofs option.
% 2.12/2.33
% 2.12/2.33 ============ end of search ============
% 2.12/2.33
% 2.12/2.33 -------------- statistics -------------
% 2.12/2.33 clauses given 162
% 2.12/2.33 clauses generated 27510
% 2.12/2.33 clauses kept 3167
% 2.12/2.33 clauses forward subsumed 13623
% 2.12/2.33 clauses back subsumed 166
% 2.12/2.33 Kbytes malloced 4882
% 2.12/2.33
% 2.12/2.33 ----------- times (seconds) -----------
% 2.12/2.33 user CPU time 0.45 (0 hr, 0 min, 0 sec)
% 2.12/2.33 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.12/2.33 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.12/2.33
% 2.12/2.33 That finishes the proof of the theorem.
% 2.12/2.33
% 2.12/2.33 Process 19320 finished Wed Jul 27 08:56:54 2022
% 2.12/2.33 Otter interrupted
% 2.12/2.33 PROOF FOUND
%------------------------------------------------------------------------------