TSTP Solution File: ALG007-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 2.26s 2.42s
% Output : Refutation 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 4 RR)
% Number of literals : 40 ( 39 equ; 3 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
file('ALG007-1.p',unknown),
[] ).
cnf(2,plain,
difference(difference(a,c),difference(b,c)) != difference(difference(a,b),c),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(5,axiom,
difference(A,difference(B,A)) = A,
file('ALG007-1.p',unknown),
[] ).
cnf(6,axiom,
difference(A,difference(A,B)) = difference(B,difference(B,A)),
file('ALG007-1.p',unknown),
[] ).
cnf(7,axiom,
difference(difference(A,B),C) = difference(difference(A,C),B),
file('ALG007-1.p',unknown),
[] ).
cnf(8,plain,
difference(difference(A,B),B) = difference(A,B),
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.2,4.1.1')] ).
cnf(10,plain,
difference(difference(A,B),difference(A,B)) = difference(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,8]),5]),
[iquote('para_into,6.1.1.2,8.1.1,demod,5')] ).
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)],[6,6])]),
[iquote('para_into,6.1.1.2,6.1.1,flip.1')] ).
cnf(18,plain,
difference(difference(difference(A,B),C),B) = difference(difference(A,B),C),
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(21,plain,
difference(difference(A,difference(A,B)),C) = difference(difference(B,C),difference(B,A)),
inference(para_into,[status(thm),theory(equality)],[7,6]),
[iquote('para_into,7.1.1.1,6.1.1')] ).
cnf(23,plain,
difference(difference(A,B),difference(C,A)) = difference(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,5])]),
[iquote('para_into,7.1.1.1,4.1.1,flip.1')] ).
cnf(24,plain,
difference(difference(A,difference(difference(A,B),C)),B) = difference(C,difference(C,difference(A,B))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,6])]),
[iquote('para_into,7.1.1,6.1.1,flip.1')] ).
cnf(29,plain,
difference(difference(A,B),difference(A,C)) = difference(difference(C,difference(C,A)),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
[iquote('copy,21,flip.1')] ).
cnf(31,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]),23])]),
[iquote('back_demod,12,demod,23,flip.1')] ).
cnf(32,plain,
difference(difference(A,B),difference(difference(A,C),B)) = difference(C,difference(C,difference(A,B))),
inference(para_from,[status(thm),theory(equality)],[7,6]),
[iquote('para_from,7.1.1,6.1.1.2')] ).
cnf(34,plain,
difference(A,difference(difference(B,A),C)) = A,
inference(para_from,[status(thm),theory(equality)],[7,5]),
[iquote('para_from,7.1.1,4.1.1.2')] ).
cnf(36,plain,
difference(difference(a,difference(b,c)),c) != difference(difference(a,b),c),
inference(para_from,[status(thm),theory(equality)],[7,2]),
[iquote('para_from,7.1.1,2.1.1')] ).
cnf(38,plain,
difference(difference(difference(A,B),C),difference(difference(A,C),B)) = difference(B,B),
inference(para_into,[status(thm),theory(equality)],[10,7]),
[iquote('para_into,10.1.1.1,7.1.1')] ).
cnf(41,plain,
difference(A,A) = difference(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,7]),38]),
[iquote('para_into,10.1.1.2,7.1.1,demod,38')] ).
cnf(45,plain,
difference(difference(A,A),B) = difference(difference(C,B),C),
inference(para_from,[status(thm),theory(equality)],[41,7]),
[iquote('para_from,41.1.1,7.1.1.1')] ).
cnf(47,plain,
difference(A,difference(B,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[41,6]),5]),
[iquote('para_from,41.1.1,6.1.1.2,demod,5')] ).
cnf(49,plain,
difference(difference(A,B),A) = difference(difference(C,C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[45])]),
[iquote('copy,45,flip.1')] ).
cnf(52,plain,
difference(difference(A,A),B) = difference(A,A),
inference(para_from,[status(thm),theory(equality)],[47,5]),
[iquote('para_from,46.1.1,4.1.1.2')] ).
cnf(53,plain,
difference(difference(A,B),A) = difference(C,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[49]),52]),
[iquote('back_demod,49,demod,52')] ).
cnf(61,plain,
difference(difference(A,B),difference(B,C)) = difference(A,B),
inference(para_into,[status(thm),theory(equality)],[34,5]),
[iquote('para_into,34.1.1.2.1,4.1.1')] ).
cnf(80,plain,
difference(A,difference(A,difference(A,B))) = difference(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[53,6]),47])]),
[iquote('para_from,53.1.1,6.1.1.2,demod,47,flip.1')] ).
cnf(98,plain,
difference(difference(difference(A,B),C),difference(D,difference(A,C))) = difference(difference(A,C),B),
inference(para_into,[status(thm),theory(equality)],[23,7]),
[iquote('para_into,22.1.1.1,7.1.1')] ).
cnf(102,plain,
difference(difference(difference(A,B),C),difference(D,A)) = difference(difference(A,B),C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[23,18]),23]),
[iquote('para_from,22.1.1,18.1.1.1.1,demod,23')] ).
cnf(209,plain,
difference(difference(A,difference(B,C)),B) = difference(A,B),
inference(para_into,[status(thm),theory(equality)],[61,7]),
[iquote('para_into,61.1.1,7.1.1')] ).
cnf(223,plain,
difference(difference(A,difference(B,C)),difference(A,C)) = difference(C,difference(C,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[21,23])]),
[iquote('para_into,21.1.1,22.1.1,flip.1')] ).
cnf(226,plain,
difference(difference(A,B),difference(A,C)) = difference(difference(C,B),difference(C,A)),
inference(para_into,[status(thm),theory(equality)],[21,7]),
[iquote('para_into,21.1.1,7.1.1')] ).
cnf(766,plain,
difference(difference(A,B),difference(difference(A,B),difference(difference(C,difference(C,A)),B))) = difference(difference(A,B),difference(A,C)),
inference(para_from,[status(thm),theory(equality)],[29,80]),
[iquote('para_from,29.1.1,80.1.1.2.2')] ).
cnf(982,plain,
difference(A,difference(A,difference(B,C))) = difference(difference(B,C),difference(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[32,209]),23]),
[iquote('para_from,32.1.1,209.1.1.1,demod,23')] ).
cnf(2647,plain,
difference(difference(A,B),difference(A,difference(A,C))) = difference(difference(A,B),C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[98,80]),98])]),
[iquote('para_into,97.1.1.1.1,80.1.1,demod,98,flip.1')] ).
cnf(3139,plain,
difference(difference(A,difference(A,B)),C) = difference(A,difference(A,difference(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[223,29]),102]),
[iquote('para_into,223.1.1.1,29.1.1,demod,102')] ).
cnf(3453,plain,
difference(difference(A,B),difference(difference(A,B),C)) = difference(difference(A,B),difference(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[766]),3139,31]),
[iquote('back_demod,766,demod,3139,31')] ).
cnf(4583,plain,
difference(difference(A,difference(difference(B,C),difference(B,A))),C) = difference(difference(A,B),C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[226,24]),3453,2647]),
[iquote('para_from,226.1.1,24.1.1.1.2,demod,3453,2647')] ).
cnf(4598,plain,
difference(A,difference(difference(B,C),difference(B,A))) = difference(A,difference(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[982,982]),47]),
[iquote('para_into,982.1.1.2,982.1.1,demod,47')] ).
cnf(4599,plain,
difference(difference(A,difference(B,C)),C) = difference(difference(A,B),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4583]),4598]),
[iquote('back_demod,4583,demod,4598')] ).
cnf(4601,plain,
$false,
inference(binary,[status(thm)],[4599,36]),
[iquote('binary,4599.1,36.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 03:41:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.26/2.42 ----- Otter 3.3f, August 2004 -----
% 2.26/2.42 The process was started by sandbox on n009.cluster.edu,
% 2.26/2.42 Wed Jul 27 03:41:36 2022
% 2.26/2.42 The command was "./otter". The process ID is 13160.
% 2.26/2.42
% 2.26/2.42 set(prolog_style_variables).
% 2.26/2.42 set(auto).
% 2.26/2.42 dependent: set(auto1).
% 2.26/2.42 dependent: set(process_input).
% 2.26/2.42 dependent: clear(print_kept).
% 2.26/2.42 dependent: clear(print_new_demod).
% 2.26/2.42 dependent: clear(print_back_demod).
% 2.26/2.42 dependent: clear(print_back_sub).
% 2.26/2.42 dependent: set(control_memory).
% 2.26/2.42 dependent: assign(max_mem, 12000).
% 2.26/2.42 dependent: assign(pick_given_ratio, 4).
% 2.26/2.42 dependent: assign(stats_level, 1).
% 2.26/2.42 dependent: assign(max_seconds, 10800).
% 2.26/2.42 clear(print_given).
% 2.26/2.42
% 2.26/2.42 list(usable).
% 2.26/2.42 0 [] A=A.
% 2.26/2.42 0 [] difference(X,difference(Y,X))=X.
% 2.26/2.42 0 [] difference(X,difference(X,Y))=difference(Y,difference(Y,X)).
% 2.26/2.42 0 [] difference(difference(X,Y),Z)=difference(difference(X,Z),Y).
% 2.26/2.42 0 [] difference(difference(a,b),c)!=difference(difference(a,c),difference(b,c)).
% 2.26/2.42 end_of_list.
% 2.26/2.42
% 2.26/2.42 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.26/2.42
% 2.26/2.42 All clauses are units, and equality is present; the
% 2.26/2.42 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.26/2.42
% 2.26/2.42 dependent: set(knuth_bendix).
% 2.26/2.42 dependent: set(anl_eq).
% 2.26/2.42 dependent: set(para_from).
% 2.26/2.42 dependent: set(para_into).
% 2.26/2.42 dependent: clear(para_from_right).
% 2.26/2.42 dependent: clear(para_into_right).
% 2.26/2.42 dependent: set(para_from_vars).
% 2.26/2.42 dependent: set(eq_units_both_ways).
% 2.26/2.42 dependent: set(dynamic_demod_all).
% 2.26/2.42 dependent: set(dynamic_demod).
% 2.26/2.42 dependent: set(order_eq).
% 2.26/2.42 dependent: set(back_demod).
% 2.26/2.42 dependent: set(lrpo).
% 2.26/2.42
% 2.26/2.42 ------------> process usable:
% 2.26/2.42 ** KEPT (pick-wt=13): 2 [copy,1,flip.1] difference(difference(a,c),difference(b,c))!=difference(difference(a,b),c).
% 2.26/2.42
% 2.26/2.42 ------------> process sos:
% 2.26/2.42 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.26/2.42 ** KEPT (pick-wt=7): 4 [] difference(A,difference(B,A))=A.
% 2.26/2.42 ---> New Demodulator: 5 [new_demod,4] difference(A,difference(B,A))=A.
% 2.26/2.42 ** KEPT (pick-wt=11): 6 [] difference(A,difference(A,B))=difference(B,difference(B,A)).
% 2.26/2.42 ** KEPT (pick-wt=11): 7 [] difference(difference(A,B),C)=difference(difference(A,C),B).
% 2.26/2.42 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.26/2.42 >>>> Starting back demodulation with 5.
% 2.26/2.42 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] difference(A,difference(A,B))=difference(B,difference(B,A)).
% 2.26/2.42 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] difference(difference(A,B),C)=difference(difference(A,C),B).
% 2.26/2.42
% 2.26/2.42 ======= end of input processing =======
% 2.26/2.42
% 2.26/2.42 =========== start of search ===========
% 2.26/2.42
% 2.26/2.42
% 2.26/2.42 Resetting weight limit to 17.
% 2.26/2.42
% 2.26/2.42
% 2.26/2.42 Resetting weight limit to 17.
% 2.26/2.42
% 2.26/2.42 sos_size=995
% 2.26/2.42
% 2.26/2.42 -------- PROOF --------
% 2.26/2.42
% 2.26/2.42 ----> UNIT CONFLICT at 0.51 sec ----> 4601 [binary,4599.1,36.1] $F.
% 2.26/2.42
% 2.26/2.42 Length of proof is 35. Level of proof is 12.
% 2.26/2.42
% 2.26/2.42 ---------------- PROOF ----------------
% 2.26/2.42 % SZS status Unsatisfiable
% 2.26/2.42 % SZS output start Refutation
% See solution above
% 2.26/2.42 ------------ end of proof -------------
% 2.26/2.42
% 2.26/2.42
% 2.26/2.42 Search stopped by max_proofs option.
% 2.26/2.42
% 2.26/2.42
% 2.26/2.42 Search stopped by max_proofs option.
% 2.26/2.42
% 2.26/2.42 ============ end of search ============
% 2.26/2.42
% 2.26/2.42 -------------- statistics -------------
% 2.26/2.42 clauses given 100
% 2.26/2.42 clauses generated 21580
% 2.26/2.42 clauses kept 3101
% 2.26/2.42 clauses forward subsumed 20722
% 2.26/2.42 clauses back subsumed 61
% 2.26/2.42 Kbytes malloced 4882
% 2.26/2.42
% 2.26/2.42 ----------- times (seconds) -----------
% 2.26/2.42 user CPU time 0.51 (0 hr, 0 min, 0 sec)
% 2.26/2.42 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.26/2.42 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.26/2.42
% 2.26/2.42 That finishes the proof of the theorem.
% 2.26/2.42
% 2.26/2.42 Process 13160 finished Wed Jul 27 03:41:38 2022
% 2.26/2.42 Otter interrupted
% 2.26/2.42 PROOF FOUND
%------------------------------------------------------------------------------