TSTP Solution File: LAT031-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT031-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:01:49 EDT 2022
% Result : Unsatisfiable 1.68s 1.93s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 6 RR)
% Number of literals : 30 ( 29 equ; 5 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 : 61 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
join(xx,meet(yy,zz)) != meet(join(xx,yy),join(xx,zz)),
file('LAT031-1.p',unknown),
[] ).
cnf(2,plain,
meet(join(xx,yy),join(xx,zz)) != join(xx,meet(yy,zz)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
meet(A,A) = A,
file('LAT031-1.p',unknown),
[] ).
cnf(11,axiom,
join(A,meet(A,B)) = A,
file('LAT031-1.p',unknown),
[] ).
cnf(12,axiom,
meet(A,B) = meet(B,A),
file('LAT031-1.p',unknown),
[] ).
cnf(13,axiom,
join(A,B) = join(B,A),
file('LAT031-1.p',unknown),
[] ).
cnf(14,axiom,
meet(meet(A,B),C) = meet(A,meet(B,C)),
file('LAT031-1.p',unknown),
[] ).
cnf(17,axiom,
join(join(A,B),C) = join(A,join(B,C)),
file('LAT031-1.p',unknown),
[] ).
cnf(19,axiom,
meet(A,join(B,C)) = join(meet(A,B),meet(A,C)),
file('LAT031-1.p',unknown),
[] ).
cnf(20,plain,
join(meet(join(xx,yy),xx),meet(join(xx,yy),zz)) != join(xx,meet(yy,zz)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),19]),
[iquote('back_demod,2,demod,19')] ).
cnf(21,plain,
join(A,meet(B,A)) = A,
inference(para_from,[status(thm),theory(equality)],[12,11]),
[iquote('para_from,12.1.1,10.1.1.2')] ).
cnf(25,plain,
join(meet(A,B),B) = B,
inference(para_into,[status(thm),theory(equality)],[21,13]),
[iquote('para_into,21.1.1,13.1.1')] ).
cnf(28,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,4])]),
[iquote('para_into,14.1.1.1,4.1.1,flip.1')] ).
cnf(42,plain,
join(meet(A,B),join(B,C)) = join(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,25])]),
[iquote('para_into,16.1.1.1,25.1.1,flip.1')] ).
cnf(48,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,13]),17]),
[iquote('para_into,16.1.1.1,13.1.1,demod,17')] ).
cnf(55,plain,
join(A,join(B,C)) = join(B,join(C,A)),
inference(para_into,[status(thm),theory(equality)],[17,13]),
[iquote('para_into,16.1.1,13.1.1')] ).
cnf(60,plain,
join(A,join(B,C)) = join(C,join(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[55])]),
[iquote('copy,55,flip.1')] ).
cnf(63,plain,
meet(A,meet(B,A)) = meet(A,B),
inference(para_into,[status(thm),theory(equality)],[28,12]),
[iquote('para_into,28.1.1.2,12.1.1')] ).
cnf(91,plain,
meet(join(A,B),C) = join(meet(C,A),meet(C,B)),
inference(para_into,[status(thm),theory(equality)],[19,12]),
[iquote('para_into,18.1.1,12.1.1')] ).
cnf(94,plain,
join(meet(A,B),meet(A,C)) = meet(join(B,C),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[91])]),
[iquote('copy,91,flip.1')] ).
cnf(107,plain,
join(meet(A,B),meet(B,A)) = meet(A,B),
inference(para_from,[status(thm),theory(equality)],[63,21]),
[iquote('para_from,63.1.1,21.1.1.2')] ).
cnf(174,plain,
join(meet(A,B),join(meet(B,A),C)) = join(meet(B,A),C),
inference(para_into,[status(thm),theory(equality)],[42,63]),
[iquote('para_into,42.1.1.1,63.1.1')] ).
cnf(184,plain,
join(meet(A,B),join(C,B)) = join(B,C),
inference(para_into,[status(thm),theory(equality)],[42,13]),
[iquote('para_into,42.1.1.2,13.1.1')] ).
cnf(348,plain,
join(meet(A,B),join(C,meet(B,A))) = join(C,meet(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[107,60])]),
[iquote('para_from,107.1.1,60.1.1.2,flip.1')] ).
cnf(349,plain,
join(A,meet(B,C)) = join(meet(C,B),A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[107,55]),174]),
[iquote('para_from,107.1.1,55.1.1.2,demod,174')] ).
cnf(350,plain,
join(A,meet(B,C)) = join(A,meet(C,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[107,48]),348]),
[iquote('para_from,107.1.1,48.1.1.2,demod,348')] ).
cnf(615,plain,
join(meet(zz,xx),join(meet(zz,yy),meet(join(xx,yy),xx))) != join(xx,meet(yy,zz)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[349,20]),19,17]),
[iquote('para_from,349.1.1,20.1.1,demod,19,17')] ).
cnf(756,plain,
meet(join(A,B),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[94,4]),11])]),
[iquote('para_into,94.1.1.1,4.1.1,demod,11,flip.1')] ).
cnf(777,plain,
join(xx,meet(zz,yy)) != join(xx,meet(yy,zz)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[615]),756,184]),
[iquote('back_demod,615,demod,756,184')] ).
cnf(778,plain,
$false,
inference(binary,[status(thm)],[777,350]),
[iquote('binary,777.1,350.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT031-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n021.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
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 08:06:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.68/1.92 ----- Otter 3.3f, August 2004 -----
% 1.68/1.92 The process was started by sandbox2 on n021.cluster.edu,
% 1.68/1.92 Wed Jul 27 08:06:23 2022
% 1.68/1.92 The command was "./otter". The process ID is 20463.
% 1.68/1.92
% 1.68/1.92 set(prolog_style_variables).
% 1.68/1.92 set(auto).
% 1.68/1.92 dependent: set(auto1).
% 1.68/1.92 dependent: set(process_input).
% 1.68/1.92 dependent: clear(print_kept).
% 1.68/1.92 dependent: clear(print_new_demod).
% 1.68/1.92 dependent: clear(print_back_demod).
% 1.68/1.92 dependent: clear(print_back_sub).
% 1.68/1.92 dependent: set(control_memory).
% 1.68/1.92 dependent: assign(max_mem, 12000).
% 1.68/1.92 dependent: assign(pick_given_ratio, 4).
% 1.68/1.92 dependent: assign(stats_level, 1).
% 1.68/1.92 dependent: assign(max_seconds, 10800).
% 1.68/1.92 clear(print_given).
% 1.68/1.92
% 1.68/1.92 list(usable).
% 1.68/1.92 0 [] A=A.
% 1.68/1.92 0 [] meet(X,X)=X.
% 1.68/1.92 0 [] join(X,X)=X.
% 1.68/1.92 0 [] meet(X,join(X,Y))=X.
% 1.68/1.92 0 [] join(X,meet(X,Y))=X.
% 1.68/1.92 0 [] meet(X,Y)=meet(Y,X).
% 1.68/1.92 0 [] join(X,Y)=join(Y,X).
% 1.68/1.92 0 [] meet(meet(X,Y),Z)=meet(X,meet(Y,Z)).
% 1.68/1.92 0 [] join(join(X,Y),Z)=join(X,join(Y,Z)).
% 1.68/1.92 0 [] meet(X,join(Y,Z))=join(meet(X,Y),meet(X,Z)).
% 1.68/1.92 0 [] join(xx,meet(yy,zz))!=meet(join(xx,yy),join(xx,zz)).
% 1.68/1.92 end_of_list.
% 1.68/1.92
% 1.68/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.68/1.92
% 1.68/1.92 All clauses are units, and equality is present; the
% 1.68/1.92 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.68/1.92
% 1.68/1.92 dependent: set(knuth_bendix).
% 1.68/1.92 dependent: set(anl_eq).
% 1.68/1.92 dependent: set(para_from).
% 1.68/1.92 dependent: set(para_into).
% 1.68/1.92 dependent: clear(para_from_right).
% 1.68/1.92 dependent: clear(para_into_right).
% 1.68/1.92 dependent: set(para_from_vars).
% 1.68/1.92 dependent: set(eq_units_both_ways).
% 1.68/1.92 dependent: set(dynamic_demod_all).
% 1.68/1.92 dependent: set(dynamic_demod).
% 1.68/1.92 dependent: set(order_eq).
% 1.68/1.92 dependent: set(back_demod).
% 1.68/1.92 dependent: set(lrpo).
% 1.68/1.92
% 1.68/1.92 ------------> process usable:
% 1.68/1.92 ** KEPT (pick-wt=13): 2 [copy,1,flip.1] meet(join(xx,yy),join(xx,zz))!=join(xx,meet(yy,zz)).
% 1.68/1.92
% 1.68/1.92 ------------> process sos:
% 1.68/1.92 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.68/1.92 ** KEPT (pick-wt=5): 4 [] meet(A,A)=A.
% 1.68/1.92 ---> New Demodulator: 5 [new_demod,4] meet(A,A)=A.
% 1.68/1.92 ** KEPT (pick-wt=5): 6 [] join(A,A)=A.
% 1.68/1.92 ---> New Demodulator: 7 [new_demod,6] join(A,A)=A.
% 1.68/1.92 ** KEPT (pick-wt=7): 8 [] meet(A,join(A,B))=A.
% 1.68/1.92 ---> New Demodulator: 9 [new_demod,8] meet(A,join(A,B))=A.
% 1.68/1.92 ** KEPT (pick-wt=7): 10 [] join(A,meet(A,B))=A.
% 1.68/1.92 ---> New Demodulator: 11 [new_demod,10] join(A,meet(A,B))=A.
% 1.68/1.92 ** KEPT (pick-wt=7): 12 [] meet(A,B)=meet(B,A).
% 1.68/1.92 ** KEPT (pick-wt=7): 13 [] join(A,B)=join(B,A).
% 1.68/1.92 ** KEPT (pick-wt=11): 14 [] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 1.68/1.92 ---> New Demodulator: 15 [new_demod,14] meet(meet(A,B),C)=meet(A,meet(B,C)).
% 1.68/1.92 ** KEPT (pick-wt=11): 16 [] join(join(A,B),C)=join(A,join(B,C)).
% 1.68/1.92 ---> New Demodulator: 17 [new_demod,16] join(join(A,B),C)=join(A,join(B,C)).
% 1.68/1.92 ** KEPT (pick-wt=13): 18 [] meet(A,join(B,C))=join(meet(A,B),meet(A,C)).
% 1.68/1.92 ---> New Demodulator: 19 [new_demod,18] meet(A,join(B,C))=join(meet(A,B),meet(A,C)).
% 1.68/1.92 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.68/1.92 >>>> Starting back demodulation with 5.
% 1.68/1.92 >>>> Starting back demodulation with 7.
% 1.68/1.92 >>>> Starting back demodulation with 9.
% 1.68/1.92 >>>> Starting back demodulation with 11.
% 1.68/1.92 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] meet(A,B)=meet(B,A).
% 1.68/1.92 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] join(A,B)=join(B,A).
% 1.68/1.93 >>>> Starting back demodulation with 15.
% 1.68/1.93 >>>> Starting back demodulation with 17.
% 1.68/1.93 >>>> Starting back demodulation with 19.
% 1.68/1.93 >> back demodulating 8 with 19.
% 1.68/1.93 >> back demodulating 2 with 19.
% 1.68/1.93
% 1.68/1.93 ======= end of input processing =======
% 1.68/1.93
% 1.68/1.93 =========== start of search ===========
% 1.68/1.93
% 1.68/1.93 -------- PROOF --------
% 1.68/1.93
% 1.68/1.93 ----> UNIT CONFLICT at 0.03 sec ----> 778 [binary,777.1,350.1] $F.
% 1.68/1.93
% 1.68/1.93 Length of proof is 21. Level of proof is 7.
% 1.68/1.93
% 1.68/1.93 ---------------- PROOF ----------------
% 1.68/1.93 % SZS status Unsatisfiable
% 1.68/1.93 % SZS output start Refutation
% See solution above
% 1.68/1.93 ------------ end of proof -------------
% 1.68/1.93
% 1.68/1.93
% 1.68/1.93 Search stopped by max_proofs option.
% 1.68/1.93
% 1.68/1.93
% 1.68/1.93 Search stopped by max_proofs option.
% 1.68/1.93
% 1.68/1.93 ============ end of search ============
% 1.68/1.93
% 1.68/1.93 -------------- statistics -------------
% 1.68/1.93 clauses given 59
% 1.68/1.93 clauses generated 2835
% 1.68/1.93 clauses kept 486
% 1.68/1.93 clauses forward subsumed 2571
% 1.68/1.93 clauses back subsumed 0
% 1.68/1.93 Kbytes malloced 1953
% 1.68/1.93
% 1.68/1.93 ----------- times (seconds) -----------
% 1.68/1.93 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.68/1.93 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.68/1.93 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.68/1.93
% 1.68/1.93 That finishes the proof of the theorem.
% 1.68/1.93
% 1.68/1.93 Process 20463 finished Wed Jul 27 08:06:24 2022
% 1.68/1.93 Otter interrupted
% 1.68/1.93 PROOF FOUND
%------------------------------------------------------------------------------