TSTP Solution File: ALG006-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG006-1 : TPTP v8.1.0. Released v2.2.0.
% 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 12:45:53 EDT 2022
% Result : Unsatisfiable 1.58s 1.82s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 3 RR)
% Number of literals : 22 ( 21 equ; 2 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
difference(difference(a,c),b) != difference(difference(a,b),c),
file('ALG006-1.p',unknown),
[] ).
cnf(4,axiom,
difference(A,difference(B,A)) = A,
file('ALG006-1.p',unknown),
[] ).
cnf(5,axiom,
difference(A,difference(A,B)) = difference(B,difference(B,A)),
file('ALG006-1.p',unknown),
[] ).
cnf(6,axiom,
difference(difference(A,B),C) = difference(difference(A,C),difference(B,C)),
file('ALG006-1.p',unknown),
[] ).
cnf(7,plain,
difference(difference(A,B),difference(C,B)) = difference(difference(A,C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(8,plain,
difference(difference(A,B),B) = difference(A,B),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.2,3.1.1')] ).
cnf(11,plain,
difference(difference(A,B),difference(A,B)) = difference(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,8]),4]),
[iquote('para_into,5.1.1.2,8.1.1,demod,4')] ).
cnf(12,plain,
difference(difference(A,B),difference(difference(A,B),A)) = difference(A,difference(B,difference(B,A))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,5])]),
[iquote('para_into,5.1.1.2,5.1.1,flip.1')] ).
cnf(19,plain,
difference(difference(A,difference(A,B)),difference(B,difference(B,A))) = difference(A,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,5]),11]),
[iquote('para_into,10.1.1.1,5.1.1,demod,11')] ).
cnf(20,plain,
difference(A,A) = difference(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,5]),19,11]),
[iquote('para_into,10.1.1.2,5.1.1,demod,19,11')] ).
cnf(41,plain,
difference(difference(a,b),difference(c,b)) != difference(difference(a,b),c),
inference(para_from,[status(thm),theory(equality)],[6,1]),
[iquote('para_from,6.1.1,1.1.1')] ).
cnf(46,plain,
difference(A,difference(B,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[20,5]),4]),
[iquote('para_from,20.1.1,5.1.1.2,demod,4')] ).
cnf(53,plain,
difference(difference(A,A),B) = difference(A,A),
inference(para_from,[status(thm),theory(equality)],[46,4]),
[iquote('para_from,45.1.1,3.1.1.2')] ).
cnf(83,plain,
difference(difference(difference(A,B),C),B) = difference(difference(A,B),difference(C,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,8])]),
[iquote('para_into,7.1.1.1,8.1.1,flip.1')] ).
cnf(98,plain,
difference(difference(A,B),A) = difference(A,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,53])]),
[iquote('para_into,7.1.1,53.1.1,flip.1')] ).
cnf(104,plain,
difference(A,difference(B,difference(B,A))) = difference(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),98,46])]),
[iquote('back_demod,12,demod,98,46,flip.1')] ).
cnf(120,plain,
difference(difference(A,difference(B,C)),B) = difference(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[98,7]),46])]),
[iquote('para_from,97.1.1,7.1.1.2,demod,46,flip.1')] ).
cnf(154,plain,
difference(difference(A,B),difference(A,difference(B,C))) = difference(C,C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[120,98]),11,11]),
[iquote('para_from,120.1.1,97.1.1.1,demod,11,11')] ).
cnf(359,plain,
difference(A,difference(A,difference(difference(B,A),C))) = difference(C,C),
inference(para_into,[status(thm),theory(equality)],[154,4]),
[iquote('para_into,154.1.1.1,3.1.1')] ).
cnf(569,plain,
difference(A,difference(A,difference(difference(B,A),C))) = difference(A,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[359,104]),11,11,11]),
[iquote('para_into,359.1.1.2.2,104.1.1,demod,11,11,11')] ).
cnf(627,plain,
difference(difference(A,B),difference(C,B)) = difference(difference(A,B),C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[569,104]),46,83])]),
[iquote('para_from,569.1.1,104.1.1.2,demod,46,83,flip.1')] ).
cnf(629,plain,
$false,
inference(binary,[status(thm)],[627,41]),
[iquote('binary,627.1,41.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG006-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 04:02:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.58/1.82 ----- Otter 3.3f, August 2004 -----
% 1.58/1.82 The process was started by sandbox2 on n019.cluster.edu,
% 1.58/1.82 Wed Jul 27 04:02:22 2022
% 1.58/1.82 The command was "./otter". The process ID is 1346.
% 1.58/1.82
% 1.58/1.82 set(prolog_style_variables).
% 1.58/1.82 set(auto).
% 1.58/1.82 dependent: set(auto1).
% 1.58/1.82 dependent: set(process_input).
% 1.58/1.82 dependent: clear(print_kept).
% 1.58/1.82 dependent: clear(print_new_demod).
% 1.58/1.82 dependent: clear(print_back_demod).
% 1.58/1.82 dependent: clear(print_back_sub).
% 1.58/1.82 dependent: set(control_memory).
% 1.58/1.82 dependent: assign(max_mem, 12000).
% 1.58/1.82 dependent: assign(pick_given_ratio, 4).
% 1.58/1.82 dependent: assign(stats_level, 1).
% 1.58/1.82 dependent: assign(max_seconds, 10800).
% 1.58/1.82 clear(print_given).
% 1.58/1.82
% 1.58/1.82 list(usable).
% 1.58/1.82 0 [] A=A.
% 1.58/1.82 0 [] difference(X,difference(Y,X))=X.
% 1.58/1.82 0 [] difference(X,difference(X,Y))=difference(Y,difference(Y,X)).
% 1.58/1.82 0 [] difference(difference(X,Y),Z)=difference(difference(X,Z),difference(Y,Z)).
% 1.58/1.82 0 [] difference(difference(a,c),b)!=difference(difference(a,b),c).
% 1.58/1.82 end_of_list.
% 1.58/1.82
% 1.58/1.82 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.58/1.82
% 1.58/1.82 All clauses are units, and equality is present; the
% 1.58/1.82 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.58/1.82
% 1.58/1.82 dependent: set(knuth_bendix).
% 1.58/1.82 dependent: set(anl_eq).
% 1.58/1.82 dependent: set(para_from).
% 1.58/1.82 dependent: set(para_into).
% 1.58/1.82 dependent: clear(para_from_right).
% 1.58/1.82 dependent: clear(para_into_right).
% 1.58/1.82 dependent: set(para_from_vars).
% 1.58/1.82 dependent: set(eq_units_both_ways).
% 1.58/1.82 dependent: set(dynamic_demod_all).
% 1.58/1.82 dependent: set(dynamic_demod).
% 1.58/1.82 dependent: set(order_eq).
% 1.58/1.82 dependent: set(back_demod).
% 1.58/1.82 dependent: set(lrpo).
% 1.58/1.82
% 1.58/1.82 ------------> process usable:
% 1.58/1.82 ** KEPT (pick-wt=11): 1 [] difference(difference(a,c),b)!=difference(difference(a,b),c).
% 1.58/1.82
% 1.58/1.82 ------------> process sos:
% 1.58/1.82 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.58/1.82 ** KEPT (pick-wt=7): 3 [] difference(A,difference(B,A))=A.
% 1.58/1.82 ---> New Demodulator: 4 [new_demod,3] difference(A,difference(B,A))=A.
% 1.58/1.82 ** KEPT (pick-wt=11): 5 [] difference(A,difference(A,B))=difference(B,difference(B,A)).
% 1.58/1.82 ** KEPT (pick-wt=13): 6 [] difference(difference(A,B),C)=difference(difference(A,C),difference(B,C)).
% 1.58/1.82 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.58/1.82 >>>> Starting back demodulation with 4.
% 1.58/1.82 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] difference(A,difference(A,B))=difference(B,difference(B,A)).
% 1.58/1.82 ** KEPT (pick-wt=13): 7 [copy,6,flip.1] difference(difference(A,B),difference(C,B))=difference(difference(A,C),B).
% 1.58/1.82 Following clause subsumed by 6 during input processing: 0 [copy,7,flip.1] difference(difference(A,B),C)=difference(difference(A,C),difference(B,C)).
% 1.58/1.82
% 1.58/1.82 ======= end of input processing =======
% 1.58/1.82
% 1.58/1.82 =========== start of search ===========
% 1.58/1.82
% 1.58/1.82 -------- PROOF --------
% 1.58/1.82
% 1.58/1.82 ----> UNIT CONFLICT at 0.04 sec ----> 629 [binary,627.1,41.1] $F.
% 1.58/1.82
% 1.58/1.82 Length of proof is 17. Level of proof is 12.
% 1.58/1.82
% 1.58/1.82 ---------------- PROOF ----------------
% 1.58/1.82 % SZS status Unsatisfiable
% 1.58/1.82 % SZS output start Refutation
% See solution above
% 1.58/1.82 ------------ end of proof -------------
% 1.58/1.82
% 1.58/1.82
% 1.58/1.82 Search stopped by max_proofs option.
% 1.58/1.82
% 1.58/1.82
% 1.58/1.82 Search stopped by max_proofs option.
% 1.58/1.82
% 1.58/1.82 ============ end of search ============
% 1.58/1.82
% 1.58/1.82 -------------- statistics -------------
% 1.58/1.82 clauses given 30
% 1.58/1.82 clauses generated 1649
% 1.58/1.82 clauses kept 377
% 1.58/1.82 clauses forward subsumed 1465
% 1.58/1.82 clauses back subsumed 1
% 1.58/1.82 Kbytes malloced 1953
% 1.58/1.82
% 1.58/1.82 ----------- times (seconds) -----------
% 1.58/1.82 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.58/1.82 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.58/1.82 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.58/1.82
% 1.58/1.82 That finishes the proof of the theorem.
% 1.58/1.82
% 1.58/1.82 Process 1346 finished Wed Jul 27 04:02:23 2022
% 1.58/1.82 Otter interrupted
% 1.58/1.82 PROOF FOUND
%------------------------------------------------------------------------------