%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT045-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 13:01:51 EDT 2022
% Result : Unsatisfiable 1.84s 2.05s
% Output : Refutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 2 RR)
% Number of literals : 12 ( 11 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
join(a,meet(complement(a),join(a,b))) != join(a,b),
file('LAT045-1.p',unknown),
[] ).
cnf(7,axiom,
meet(A,join(A,B)) = A,
file('LAT045-1.p',unknown),
[] ).
cnf(11,axiom,
meet(A,B) = meet(B,A),
file('LAT045-1.p',unknown),
[] ).
cnf(21,axiom,
join(complement(A),A) = n1,
file('LAT045-1.p',unknown),
[] ).
cnf(25,axiom,
complement(complement(A)) = A,
file('LAT045-1.p',unknown),
[] ).
cnf(27,axiom,
join(A,meet(B,join(A,C))) = meet(join(A,B),join(A,C)),
file('LAT045-1.p',unknown),
[] ).
cnf(28,plain,
meet(join(A,B),join(A,C)) = join(A,meet(B,join(A,C))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[27])]),
[iquote('copy,27,flip.1')] ).
cnf(30,plain,
join(A,complement(A)) = n1,
inference(para_into,[status(thm),theory(equality)],[21,25]),
[iquote('para_into,21.1.1.1,25.1.1')] ).
cnf(36,plain,
meet(A,n1) = A,
inference(para_from,[status(thm),theory(equality)],[30,7]),
[iquote('para_from,30.1.1,7.1.1.2')] ).
cnf(51,plain,
meet(n1,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,36])]),
[iquote('para_into,11.1.1,36.1.1,flip.1')] ).
cnf(239,plain,
join(A,meet(complement(A),join(A,B))) = join(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,30]),51])]),
[iquote('para_into,28.1.1.1,30.1.1,demod,51,flip.1')] ).
cnf(241,plain,
$false,
inference(binary,[status(thm)],[239,1]),
[iquote('binary,239.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT045-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 08:23:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.84/2.04 ----- Otter 3.3f, August 2004 -----
% 1.84/2.04 The process was started by sandbox on n011.cluster.edu,
% 1.84/2.04 Wed Jul 27 08:23:10 2022
% 1.84/2.04 The command was "./otter". The process ID is 20881.
% 1.84/2.04
% 1.84/2.04 set(prolog_style_variables).
% 1.84/2.04 set(auto).
% 1.84/2.04 dependent: set(auto1).
% 1.84/2.04 dependent: set(process_input).
% 1.84/2.04 dependent: clear(print_kept).
% 1.84/2.04 dependent: clear(print_new_demod).
% 1.84/2.04 dependent: clear(print_back_demod).
% 1.84/2.04 dependent: clear(print_back_sub).
% 1.84/2.04 dependent: set(control_memory).
% 1.84/2.04 dependent: assign(max_mem, 12000).
% 1.84/2.04 dependent: assign(pick_given_ratio, 4).
% 1.84/2.04 dependent: assign(stats_level, 1).
% 1.84/2.04 dependent: assign(max_seconds, 10800).
% 1.84/2.04 clear(print_given).
% 1.84/2.04
% 1.84/2.04 list(usable).
% 1.84/2.04 0 [] A=A.
% 1.84/2.04 0 [] meet(X,X)=X.
% 1.84/2.04 0 [] join(X,X)=X.
% 1.84/2.04 0 [] meet(X,join(X,Y))=X.
% 1.84/2.04 0 [] join(X,meet(X,Y))=X.
% 1.84/2.04 0 [] meet(X,Y)=meet(Y,X).
% 1.84/2.04 0 [] join(X,Y)=join(Y,X).
% 1.84/2.04 0 [] meet(meet(X,Y),Z)=meet(X,meet(Y,Z)).
% 1.84/2.04 0 [] join(join(X,Y),Z)=join(X,join(Y,Z)).
% 1.84/2.04 0 [] complement(join(X,Y))=meet(complement(X),complement(Y)).
% 1.84/2.04 0 [] complement(meet(X,Y))=join(complement(X),complement(Y)).
% 1.84/2.04 0 [] join(complement(X),X)=n1.
% 1.84/2.04 0 [] meet(complement(X),X)=n0.
% 1.84/2.04 0 [] complement(complement(X))=X.
% 1.84/2.04 0 [] join(X,meet(Y,join(X,Z)))=meet(join(X,Y),join(X,Z)).
% 1.84/2.04 0 [] join(a,meet(complement(a),join(a,b)))!=join(a,b).
% 1.84/2.04 end_of_list.
% 1.84/2.04
% 1.84/2.04 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.84/2.04
% 1.84/2.04 All clauses are units, and equality is present; the
% 1.84/2.04 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.84/2.04
% 1.84/2.04 dependent: set(knuth_bendix).
% 1.84/2.04 dependent: set(anl_eq).
% 1.84/2.04 dependent: set(para_from).
% 1.84/2.04 dependent: set(para_into).
% 1.84/2.04 dependent: clear(para_from_right).
% 1.84/2.04 dependent: clear(para_into_right).
% 1.84/2.04 dependent: set(para_from_vars).
% 1.84/2.04 dependent: set(eq_units_both_ways).
% 1.84/2.04 dependent: set(dynamic_demod_all).
% 1.84/2.04 dependent: set(dynamic_demod).
% 1.84/2.04 dependent: set(order_eq).
% 1.84/2.04 dependent: set(back_demod).
% 1.84/2.04 dependent: set(lrpo).
% 1.84/2.04
% 1.84/2.04 ------------> process usable:
% 1.84/2.04 ** KEPT (pick-wt=12): 1 [] join(a,meet(complement(a),join(a,b)))!=join(a,b).
% 1.84/2.04
% 1.84/2.04 ------------> process sos:
% 1.84/2.04 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.84/2.04 ** KEPT (pick-wt=5): 3 [] meet(A,A)=A.
% 1.84/2.04 ---> New Demodulator: 4 [new_demod,3] meet(A,A)=A.
% 1.84/2.04 ** KEPT (pick-wt=5): 5 [] join(A,A)=A.
% 1.84/2.04 ---> New Demodulator: 6 [new_demod,5] join(A,A)=A.
% 1.84/2.04 ** KEPT (pick-wt=7): 7 [] meet(A,join(A,B))=A.
% 1.84/2.04 ---> New Demodulator: 8 [new_demod,7] meet(A,join(A,B))=A.
% 1.84/2.04 ** KEPT (pick-wt=7): 9 [] join(A,meet(A,B))=A.
% 1.84/2.04 ---> New Demodulator: 10 [new_demod,9] join(A,meet(A,B))=A.
% 1.84/2.04 ** KEPT (pick-wt=7): 11 [] meet(A,B)=meet(B,A).
% 1.84/2.04 ** KEPT (pick-wt=7): 12 [] join(A,B)=join(B,A).
% 1.84/2.04 ** KEPT (pick-wt=11): 13 [] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 1.84/2.04 ---> New Demodulator: 14 [new_demod,13] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 1.84/2.04 ** KEPT (pick-wt=11): 15 [] join(join(A,B),C)=join(A,join(B,C)).
% 1.84/2.04 ---> New Demodulator: 16 [new_demod,15] join(join(A,B),C)=join(A,join(B,C)).
% 1.84/2.04 ** KEPT (pick-wt=10): 17 [] complement(join(A,B))=meet(complement(A),complement(B)).
% 1.84/2.04 ---> New Demodulator: 18 [new_demod,17] complement(join(A,B))=meet(complement(A),complement(B)).
% 1.84/2.04 ** KEPT (pick-wt=10): 19 [] complement(meet(A,B))=join(complement(A),complement(B)).
% 1.84/2.04 ---> New Demodulator: 20 [new_demod,19] complement(meet(A,B))=join(complement(A),complement(B)).
% 1.84/2.04 ** KEPT (pick-wt=6): 21 [] join(complement(A),A)=n1.
% 1.84/2.04 ---> New Demodulator: 22 [new_demod,21] join(complement(A),A)=n1.
% 1.84/2.04 ** KEPT (pick-wt=6): 23 [] meet(complement(A),A)=n0.
% 1.84/2.04 ---> New Demodulator: 24 [new_demod,23] meet(complement(A),A)=n0.
% 1.84/2.04 ** KEPT (pick-wt=5): 25 [] complement(complement(A))=A.
% 1.84/2.04 ---> New Demodulator: 26 [new_demod,25] complement(complement(A))=A.
% 1.84/2.04 ** KEPT (pick-wt=15): 28 [copy,27,flip.1] meet(join(A,B),join(A,C))=join(A,meet(B,join(A,C))).
% 1.84/2.04 ---> New Demodulator: 29 [new_demod,28] meet(join(A,B),join(A,C))=join(A,meet(B,join(A,C))).
% 1.84/2.04 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.84/2.04 >>>> Starting back demodulation with 4.
% 1.84/2.04 >>>> Starting back demodulation with 6.
% 1.84/2.04 >>>> Starting back demodulation with 8.
% 1.84/2.04 >>>> Starting back demodulation with 10.
% 1.84/2.04 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] meet(A,B)=meet(B,A).
% 1.84/2.04 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] join(A,B)=join(B,A).
% 1.84/2.05 >>>> Starting back demodulation with 14.
% 1.84/2.05 >>>> Starting back demodulation with 16.
% 1.84/2.05 >>>> Starting back demodulation with 18.
% 1.84/2.05 >>>> Starting back demodulation with 20.
% 1.84/2.05 >>>> Starting back demodulation with 22.
% 1.84/2.05 >>>> Starting back demodulation with 24.
% 1.84/2.05 >>>> Starting back demodulation with 26.
% 1.84/2.05 >>>> Starting back demodulation with 29.
% 1.84/2.05
% 1.84/2.05 ======= end of input processing =======
% 1.84/2.05
% 1.84/2.05 =========== start of search ===========
% 1.84/2.05
% 1.84/2.05 -------- PROOF --------
% 1.84/2.05
% 1.84/2.05 ----> UNIT CONFLICT at 0.01 sec ----> 241 [binary,239.1,1.1] $F.
% 1.84/2.05
% 1.84/2.05 Length of proof is 5. Level of proof is 4.
% 1.84/2.05
% 1.84/2.05 ---------------- PROOF ----------------
% 1.84/2.05 % SZS status Unsatisfiable
% 1.84/2.05 % SZS output start Refutation
% See solution above
% 1.84/2.05 ------------ end of proof -------------
% 1.84/2.05
% 1.84/2.05
% 1.84/2.05 Search stopped by max_proofs option.
% 1.84/2.05
% 1.84/2.05
% 1.84/2.05 Search stopped by max_proofs option.
% 1.84/2.05
% 1.84/2.05 ============ end of search ============
% 1.84/2.05
% 1.84/2.05 -------------- statistics -------------
% 1.84/2.05 clauses given 46
% 1.84/2.05 clauses generated 793
% 1.84/2.05 clauses kept 126
% 1.84/2.05 clauses forward subsumed 698
% 1.84/2.05 clauses back subsumed 0
% 1.84/2.05 Kbytes malloced 1953
% 1.84/2.05
% 1.84/2.05 ----------- times (seconds) -----------
% 1.84/2.05 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.84/2.05 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.84/2.05 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.84/2.05
% 1.84/2.05 That finishes the proof of the theorem.
% 1.84/2.05
% 1.84/2.05 Process 20881 finished Wed Jul 27 08:23:12 2022
% 1.84/2.05 Otter interrupted
% 1.84/2.05 PROOF FOUND
%------------------------------------------------------------------------------