TSTP Solution File: LAT168-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT168-1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 13:02:03 EDT 2022
% Result : Unsatisfiable 4.44s 4.67s
% Output : Refutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 6 RR)
% Number of literals : 24 ( 23 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 48 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
meet(a,join(b,c)) != meet(a,join(b,meet(join(a,b),join(c,meet(a,b))))),
file('LAT168-1.p',unknown),
[] ).
cnf(2,plain,
meet(a,join(b,meet(join(a,b),join(c,meet(a,b))))) != meet(a,join(b,c)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(8,axiom,
meet(A,join(A,B)) = A,
file('LAT168-1.p',unknown),
[] ).
cnf(10,axiom,
join(A,meet(A,B)) = A,
file('LAT168-1.p',unknown),
[] ).
cnf(12,axiom,
meet(A,B) = meet(B,A),
file('LAT168-1.p',unknown),
[] ).
cnf(13,axiom,
join(A,B) = join(B,A),
file('LAT168-1.p',unknown),
[] ).
cnf(15,axiom,
meet(meet(A,B),C) = meet(A,meet(B,C)),
file('LAT168-1.p',unknown),
[] ).
cnf(17,axiom,
join(join(A,B),C) = join(A,join(B,C)),
file('LAT168-1.p',unknown),
[] ).
cnf(18,axiom,
meet(join(A,B),join(A,C)) = join(A,meet(join(A,B),meet(join(A,C),join(B,meet(A,C))))),
file('LAT168-1.p',unknown),
[] ).
cnf(19,plain,
join(A,meet(join(A,B),meet(join(A,C),join(B,meet(A,C))))) = meet(join(A,B),join(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[18])]),
[iquote('copy,18,flip.1')] ).
cnf(21,plain,
meet(join(A,B),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,8])]),
[iquote('para_into,12.1.1,8.1.1,flip.1')] ).
cnf(23,plain,
join(A,meet(B,A)) = A,
inference(para_from,[status(thm),theory(equality)],[12,10]),
[iquote('para_from,12.1.1,10.1.1.2')] ).
cnf(25,plain,
meet(join(b,meet(join(a,b),join(c,meet(a,b)))),a) != meet(a,join(b,c)),
inference(para_from,[status(thm),theory(equality)],[12,2]),
[iquote('para_from,12.1.1,2.1.1')] ).
cnf(36,plain,
meet(join(A,B),B) = B,
inference(para_into,[status(thm),theory(equality)],[21,13]),
[iquote('para_into,21.1.1.1,13.1.1')] ).
cnf(56,plain,
join(A,meet(B,meet(C,A))) = A,
inference(para_from,[status(thm),theory(equality)],[15,23]),
[iquote('para_from,14.1.1,23.1.1.2')] ).
cnf(95,plain,
meet(join(A,join(B,C)),C) = C,
inference(para_from,[status(thm),theory(equality)],[17,36]),
[iquote('para_from,16.1.1,35.1.1.1')] ).
cnf(115,plain,
join(A,join(B,meet(C,A))) = join(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[56,8]),17]),
[iquote('para_into,56.1.1.2.2,8.1.1,demod,17')] ).
cnf(144,plain,
join(A,meet(join(A,B),meet(join(A,C),join(B,meet(C,A))))) = meet(join(A,B),join(A,C)),
inference(para_into,[status(thm),theory(equality)],[19,12]),
[iquote('para_into,19.1.1.2.2.2.2,12.1.1')] ).
cnf(199,plain,
meet(join(A,B),meet(C,B)) = meet(C,B),
inference(para_into,[status(thm),theory(equality)],[95,23]),
[iquote('para_into,95.1.1.1.2,23.1.1')] ).
cnf(227,plain,
meet(join(b,meet(join(b,a),join(c,meet(a,b)))),a) != meet(a,join(b,c)),
inference(para_into,[status(thm),theory(equality)],[25,13]),
[iquote('para_into,25.1.1.1.2.1,13.1.1')] ).
cnf(855,plain,
meet(join(A,B),meet(C,join(B,meet(D,A)))) = meet(C,join(B,meet(D,A))),
inference(para_into,[status(thm),theory(equality)],[199,115]),
[iquote('para_into,199.1.1.1,115.1.1')] ).
cnf(880,plain,
join(A,meet(join(A,B),join(C,meet(B,A)))) = meet(join(A,C),join(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[144]),855]),
[iquote('back_demod,144,demod,855')] ).
cnf(1188,plain,
meet(join(b,c),a) != meet(a,join(b,c)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[880,227]),15,36]),
[iquote('para_from,880.1.1,227.1.1.1,demod,15,36')] ).
cnf(1189,plain,
$false,
inference(binary,[status(thm)],[1188,12]),
[iquote('binary,1188.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT168-1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 08:30:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.44/4.67 ----- Otter 3.3f, August 2004 -----
% 4.44/4.67 The process was started by sandbox2 on n028.cluster.edu,
% 4.44/4.67 Wed Jul 27 08:30:19 2022
% 4.44/4.67 The command was "./otter". The process ID is 7758.
% 4.44/4.67
% 4.44/4.67 set(prolog_style_variables).
% 4.44/4.67 set(auto).
% 4.44/4.67 dependent: set(auto1).
% 4.44/4.67 dependent: set(process_input).
% 4.44/4.67 dependent: clear(print_kept).
% 4.44/4.67 dependent: clear(print_new_demod).
% 4.44/4.67 dependent: clear(print_back_demod).
% 4.44/4.67 dependent: clear(print_back_sub).
% 4.44/4.67 dependent: set(control_memory).
% 4.44/4.67 dependent: assign(max_mem, 12000).
% 4.44/4.67 dependent: assign(pick_given_ratio, 4).
% 4.44/4.67 dependent: assign(stats_level, 1).
% 4.44/4.67 dependent: assign(max_seconds, 10800).
% 4.44/4.67 clear(print_given).
% 4.44/4.67
% 4.44/4.67 list(usable).
% 4.44/4.67 0 [] A=A.
% 4.44/4.67 0 [] meet(X,X)=X.
% 4.44/4.67 0 [] join(X,X)=X.
% 4.44/4.67 0 [] meet(X,join(X,Y))=X.
% 4.44/4.67 0 [] join(X,meet(X,Y))=X.
% 4.44/4.67 0 [] meet(X,Y)=meet(Y,X).
% 4.44/4.67 0 [] join(X,Y)=join(Y,X).
% 4.44/4.67 0 [] meet(meet(X,Y),Z)=meet(X,meet(Y,Z)).
% 4.44/4.67 0 [] join(join(X,Y),Z)=join(X,join(Y,Z)).
% 4.44/4.67 0 [] meet(join(X,Y),join(X,Z))=join(X,meet(join(X,Y),meet(join(X,Z),join(Y,meet(X,Z))))).
% 4.44/4.67 0 [] meet(a,join(b,c))!=meet(a,join(b,meet(join(a,b),join(c,meet(a,b))))).
% 4.44/4.67 end_of_list.
% 4.44/4.67
% 4.44/4.67 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 4.44/4.67
% 4.44/4.67 All clauses are units, and equality is present; the
% 4.44/4.67 strategy will be Knuth-Bendix with positive clauses in sos.
% 4.44/4.67
% 4.44/4.67 dependent: set(knuth_bendix).
% 4.44/4.67 dependent: set(anl_eq).
% 4.44/4.67 dependent: set(para_from).
% 4.44/4.67 dependent: set(para_into).
% 4.44/4.67 dependent: clear(para_from_right).
% 4.44/4.67 dependent: clear(para_into_right).
% 4.44/4.67 dependent: set(para_from_vars).
% 4.44/4.67 dependent: set(eq_units_both_ways).
% 4.44/4.67 dependent: set(dynamic_demod_all).
% 4.44/4.67 dependent: set(dynamic_demod).
% 4.44/4.67 dependent: set(order_eq).
% 4.44/4.67 dependent: set(back_demod).
% 4.44/4.67 dependent: set(lrpo).
% 4.44/4.67
% 4.44/4.67 ------------> process usable:
% 4.44/4.67 ** KEPT (pick-wt=19): 2 [copy,1,flip.1] meet(a,join(b,meet(join(a,b),join(c,meet(a,b)))))!=meet(a,join(b,c)).
% 4.44/4.67
% 4.44/4.67 ------------> process sos:
% 4.44/4.67 ** KEPT (pick-wt=3): 3 [] A=A.
% 4.44/4.67 ** KEPT (pick-wt=5): 4 [] meet(A,A)=A.
% 4.44/4.67 ---> New Demodulator: 5 [new_demod,4] meet(A,A)=A.
% 4.44/4.67 ** KEPT (pick-wt=5): 6 [] join(A,A)=A.
% 4.44/4.67 ---> New Demodulator: 7 [new_demod,6] join(A,A)=A.
% 4.44/4.67 ** KEPT (pick-wt=7): 8 [] meet(A,join(A,B))=A.
% 4.44/4.67 ---> New Demodulator: 9 [new_demod,8] meet(A,join(A,B))=A.
% 4.44/4.67 ** KEPT (pick-wt=7): 10 [] join(A,meet(A,B))=A.
% 4.44/4.67 ---> New Demodulator: 11 [new_demod,10] join(A,meet(A,B))=A.
% 4.44/4.67 ** KEPT (pick-wt=7): 12 [] meet(A,B)=meet(B,A).
% 4.44/4.67 ** KEPT (pick-wt=7): 13 [] join(A,B)=join(B,A).
% 4.44/4.67 ** KEPT (pick-wt=11): 14 [] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 4.44/4.67 ---> New Demodulator: 15 [new_demod,14] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 4.44/4.67 ** KEPT (pick-wt=11): 16 [] join(join(A,B),C)=join(A,join(B,C)).
% 4.44/4.67 ---> New Demodulator: 17 [new_demod,16] join(join(A,B),C)=join(A,join(B,C)).
% 4.44/4.67 ** KEPT (pick-wt=23): 19 [copy,18,flip.1] join(A,meet(join(A,B),meet(join(A,C),join(B,meet(A,C)))))=meet(join(A,B),join(A,C)).
% 4.44/4.67 ---> New Demodulator: 20 [new_demod,19] join(A,meet(join(A,B),meet(join(A,C),join(B,meet(A,C)))))=meet(join(A,B),join(A,C)).
% 4.44/4.67 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 4.44/4.67 >>>> Starting back demodulation with 5.
% 4.44/4.67 >>>> Starting back demodulation with 7.
% 4.44/4.67 >>>> Starting back demodulation with 9.
% 4.44/4.67 >>>> Starting back demodulation with 11.
% 4.44/4.67 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] meet(A,B)=meet(B,A).
% 4.44/4.67 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] join(A,B)=join(B,A).
% 4.44/4.67 >>>> Starting back demodulation with 15.
% 4.44/4.67 >>>> Starting back demodulation with 17.
% 4.44/4.67 >>>> Starting back demodulation with 20.
% 4.44/4.67
% 4.44/4.67 ======= end of input processing =======
% 4.44/4.67
% 4.44/4.67 =========== start of search ===========
% 4.44/4.67
% 4.44/4.67
% 4.44/4.67 Resetting weight limit to 13.
% 4.44/4.67
% 4.44/4.67
% 4.44/4.67 Resetting weight limit to 13.
% 4.44/4.67
% 4.44/4.67 sos_size=506
% 4.44/4.67
% 4.44/4.67 -------- PROOF --------
% 4.44/4.67
% 4.44/4.67 ----> UNIT CONFLICT at 2.88 sec ----> 1189 [binary,1188.1,12.1] $F.
% 4.44/4.67
% 4.44/4.67 Length of proof is 15. Level of proof is 7.
% 4.44/4.67
% 4.44/4.67 ---------------- PROOF ----------------
% 4.44/4.67 % SZS status Unsatisfiable
% 4.44/4.67 % SZS output start Refutation
% See solution above
% 4.44/4.67 ------------ end of proof -------------
% 4.44/4.67
% 4.44/4.67
% 4.44/4.67 Search stopped by max_proofs option.
% 4.44/4.67
% 4.44/4.67
% 4.44/4.67 Search stopped by max_proofs option.
% 4.44/4.67
% 4.44/4.67 ============ end of search ============
% 4.44/4.67
% 4.44/4.67 -------------- statistics -------------
% 4.44/4.67 clauses given 542
% 4.44/4.67 clauses generated 402331
% 4.44/4.67 clauses kept 654
% 4.44/4.67 clauses forward subsumed 156598
% 4.44/4.67 clauses back subsumed 1
% 4.44/4.67 Kbytes malloced 6835
% 4.44/4.67
% 4.44/4.67 ----------- times (seconds) -----------
% 4.44/4.67 user CPU time 2.88 (0 hr, 0 min, 2 sec)
% 4.44/4.67 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 4.44/4.67 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 4.44/4.67
% 4.44/4.67 That finishes the proof of the theorem.
% 4.44/4.67
% 4.44/4.67 Process 7758 finished Wed Jul 27 08:30:23 2022
% 4.44/4.67 Otter interrupted
% 4.44/4.67 PROOF FOUND
%------------------------------------------------------------------------------