TSTP Solution File: ALG005-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG005-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 12:45:52 EDT 2022
% Result : Unsatisfiable 1.74s 1.97s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 5 RR)
% Number of literals : 39 ( 38 equ; 4 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 : 90 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('ALG005-1.p',unknown),
[] ).
cnf(4,axiom,
difference(A,difference(B,A)) = A,
file('ALG005-1.p',unknown),
[] ).
cnf(5,axiom,
difference(A,difference(A,B)) = difference(B,difference(B,A)),
file('ALG005-1.p',unknown),
[] ).
cnf(6,axiom,
difference(difference(A,B),C) = difference(difference(A,C),difference(B,C)),
file('ALG005-1.p',unknown),
[] ).
cnf(8,axiom,
multiply(A,B) = difference(A,difference(A,B)),
file('ALG005-1.p',unknown),
[] ).
cnf(9,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(10,plain,
difference(difference(a,difference(a,b)),difference(difference(a,difference(a,b)),c)) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),8,8,8,8]),
[iquote('back_demod,1,demod,8,8,8,8')] ).
cnf(11,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(14,plain,
difference(difference(A,B),difference(A,B)) = difference(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,11]),4]),
[iquote('para_into,5.1.1.2,11.1.1,demod,4')] ).
cnf(15,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(21,plain,
difference(difference(difference(A,B),C),difference(B,C)) = difference(difference(A,B),C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,11])]),
[iquote('para_into,6.1.1.1,11.1.1,flip.1')] ).
cnf(25,plain,
difference(difference(A,B),difference(difference(C,A),B)) = difference(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,4])]),
[iquote('para_into,6.1.1.1,3.1.1,flip.1')] ).
cnf(44,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)],[14,5]),14]),
[iquote('para_into,13.1.1.1,5.1.1,demod,14')] ).
cnf(47,plain,
difference(A,A) = difference(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,5]),44,14]),
[iquote('para_into,13.1.1.2,5.1.1,demod,44,14')] ).
cnf(52,plain,
difference(A,difference(B,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[47,5]),4]),
[iquote('para_from,47.1.1,5.1.1.2,demod,4')] ).
cnf(58,plain,
difference(difference(A,A),B) = difference(A,A),
inference(para_from,[status(thm),theory(equality)],[52,4]),
[iquote('para_from,51.1.1,3.1.1.2')] ).
cnf(61,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)],[9,11])]),
[iquote('para_into,9.1.1.1,11.1.1,flip.1')] ).
cnf(66,plain,
difference(difference(A,B),difference(C,A)) = difference(A,difference(B,difference(C,A))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,4])]),
[iquote('para_into,9.1.1.1,3.1.1,flip.1')] ).
cnf(74,plain,
difference(difference(A,B),A) = difference(A,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,58])]),
[iquote('para_into,9.1.1,57.1.1,flip.1')] ).
cnf(80,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)],[15]),74,52])]),
[iquote('back_demod,15,demod,74,52,flip.1')] ).
cnf(92,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)],[74,9]),52])]),
[iquote('para_from,73.1.1,9.1.1.2,demod,52,flip.1')] ).
cnf(94,plain,
difference(difference(difference(A,B),C),A) = difference(A,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[74,9]),58])]),
[iquote('para_from,73.1.1,9.1.1.1,demod,58,flip.1')] ).
cnf(97,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)],[74,5]),52])]),
[iquote('para_from,73.1.1,5.1.1.2,demod,52,flip.1')] ).
cnf(150,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)],[92,74]),14,14]),
[iquote('para_from,92.1.1,73.1.1.1,demod,14,14')] ).
cnf(159,plain,
difference(difference(a,difference(a,b)),difference(difference(b,difference(b,a)),c)) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(para_into,[status(thm),theory(equality)],[10,5]),
[iquote('para_into,10.1.1.2.1,5.1.1')] ).
cnf(166,plain,
difference(difference(difference(A,difference(A,B)),C),B) = difference(B,B),
inference(para_into,[status(thm),theory(equality)],[94,5]),
[iquote('para_into,94.1.1.1.1,5.1.1')] ).
cnf(208,plain,
difference(difference(difference(A,difference(A,B)),C),difference(difference(B,A),C)) = difference(difference(A,difference(A,B)),C),
inference(para_into,[status(thm),theory(equality)],[25,80]),
[iquote('para_into,25.1.1.2.1,80.1.1')] ).
cnf(227,plain,
difference(difference(A,difference(A,B)),C) = difference(difference(B,difference(B,A)),C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[21,5]),208]),
[iquote('para_into,21.1.1.1.1,5.1.1,demod,208')] ).
cnf(358,plain,
difference(A,difference(A,difference(difference(B,A),C))) = difference(C,C),
inference(para_into,[status(thm),theory(equality)],[150,4]),
[iquote('para_into,150.1.1.1,3.1.1')] ).
cnf(536,plain,
difference(A,difference(A,difference(difference(B,difference(B,A)),C))) = difference(difference(B,difference(B,A)),C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[166,5]),52])]),
[iquote('para_from,166.1.1,5.1.1.2,demod,52,flip.1')] ).
cnf(568,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)],[358,80]),14,14,14]),
[iquote('para_into,358.1.1.2.2,80.1.1,demod,14,14,14')] ).
cnf(728,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)],[568,80]),52,61])]),
[iquote('para_from,568.1.1,80.1.1.2,demod,52,61,flip.1')] ).
cnf(1034,plain,
difference(A,difference(B,difference(C,A))) = difference(A,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),728,66]),
[iquote('back_demod,25,demod,728,66')] ).
cnf(1038,plain,
difference(difference(A,B),C) = difference(difference(A,C),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[9]),728]),
[iquote('back_demod,9,demod,728')] ).
cnf(1147,plain,
difference(A,difference(difference(B,difference(C,A)),D)) = difference(A,difference(B,D)),
inference(para_from,[status(thm),theory(equality)],[1038,1034]),
[iquote('para_from,1038.1.1,1034.1.1.2')] ).
cnf(1154,plain,
difference(difference(A,difference(A,B)),C) = difference(B,difference(B,difference(A,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[536]),1147])]),
[iquote('back_demod,536,demod,1147,flip.1')] ).
cnf(1178,plain,
difference(A,difference(A,difference(B,C))) = difference(B,difference(B,difference(A,C))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[227]),1154,1154]),
[iquote('back_demod,227,demod,1154,1154')] ).
cnf(1179,plain,
difference(b,difference(b,difference(a,difference(b,c)))) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[159]),1154,1154,97]),
[iquote('back_demod,159,demod,1154,1154,97')] ).
cnf(1180,plain,
$false,
inference(binary,[status(thm)],[1179,1178]),
[iquote('binary,1179.1,1178.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG005-1 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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 03:27:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.74/1.97 ----- Otter 3.3f, August 2004 -----
% 1.74/1.97 The process was started by sandbox on n007.cluster.edu,
% 1.74/1.97 Wed Jul 27 03:27:46 2022
% 1.74/1.97 The command was "./otter". The process ID is 24782.
% 1.74/1.97
% 1.74/1.97 set(prolog_style_variables).
% 1.74/1.97 set(auto).
% 1.74/1.97 dependent: set(auto1).
% 1.74/1.97 dependent: set(process_input).
% 1.74/1.97 dependent: clear(print_kept).
% 1.74/1.97 dependent: clear(print_new_demod).
% 1.74/1.97 dependent: clear(print_back_demod).
% 1.74/1.97 dependent: clear(print_back_sub).
% 1.74/1.97 dependent: set(control_memory).
% 1.74/1.97 dependent: assign(max_mem, 12000).
% 1.74/1.97 dependent: assign(pick_given_ratio, 4).
% 1.74/1.97 dependent: assign(stats_level, 1).
% 1.74/1.97 dependent: assign(max_seconds, 10800).
% 1.74/1.97 clear(print_given).
% 1.74/1.97
% 1.74/1.97 list(usable).
% 1.74/1.97 0 [] A=A.
% 1.74/1.97 0 [] difference(X,difference(Y,X))=X.
% 1.74/1.97 0 [] difference(X,difference(X,Y))=difference(Y,difference(Y,X)).
% 1.74/1.97 0 [] difference(difference(X,Y),Z)=difference(difference(X,Z),difference(Y,Z)).
% 1.74/1.97 0 [] multiply(X,Y)=difference(X,difference(X,Y)).
% 1.74/1.97 0 [] multiply(multiply(a,b),c)!=multiply(a,multiply(b,c)).
% 1.74/1.97 end_of_list.
% 1.74/1.97
% 1.74/1.97 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.74/1.97
% 1.74/1.97 All clauses are units, and equality is present; the
% 1.74/1.97 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.74/1.97
% 1.74/1.97 dependent: set(knuth_bendix).
% 1.74/1.97 dependent: set(anl_eq).
% 1.74/1.97 dependent: set(para_from).
% 1.74/1.97 dependent: set(para_into).
% 1.74/1.97 dependent: clear(para_from_right).
% 1.74/1.97 dependent: clear(para_into_right).
% 1.74/1.97 dependent: set(para_from_vars).
% 1.74/1.97 dependent: set(eq_units_both_ways).
% 1.74/1.97 dependent: set(dynamic_demod_all).
% 1.74/1.97 dependent: set(dynamic_demod).
% 1.74/1.97 dependent: set(order_eq).
% 1.74/1.97 dependent: set(back_demod).
% 1.74/1.97 dependent: set(lrpo).
% 1.74/1.97
% 1.74/1.97 ------------> process usable:
% 1.74/1.97 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a,b),c)!=multiply(a,multiply(b,c)).
% 1.74/1.97
% 1.74/1.97 ------------> process sos:
% 1.74/1.97 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.74/1.97 ** KEPT (pick-wt=7): 3 [] difference(A,difference(B,A))=A.
% 1.74/1.97 ---> New Demodulator: 4 [new_demod,3] difference(A,difference(B,A))=A.
% 1.74/1.97 ** KEPT (pick-wt=11): 5 [] difference(A,difference(A,B))=difference(B,difference(B,A)).
% 1.74/1.97 ** KEPT (pick-wt=13): 6 [] difference(difference(A,B),C)=difference(difference(A,C),difference(B,C)).
% 1.74/1.97 ** KEPT (pick-wt=9): 7 [] multiply(A,B)=difference(A,difference(A,B)).
% 1.74/1.97 ---> New Demodulator: 8 [new_demod,7] multiply(A,B)=difference(A,difference(A,B)).
% 1.74/1.97 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.74/1.97 >>>> Starting back demodulation with 4.
% 1.74/1.97 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] difference(A,difference(A,B))=difference(B,difference(B,A)).
% 1.74/1.97 ** KEPT (pick-wt=13): 9 [copy,6,flip.1] difference(difference(A,B),difference(C,B))=difference(difference(A,C),B).
% 1.74/1.97 >>>> Starting back demodulation with 8.
% 1.74/1.97 >> back demodulating 1 with 8.
% 1.74/1.97 Following clause subsumed by 6 during input processing: 0 [copy,9,flip.1] difference(difference(A,B),C)=difference(difference(A,C),difference(B,C)).
% 1.74/1.97
% 1.74/1.97 ======= end of input processing =======
% 1.74/1.97
% 1.74/1.97 =========== start of search ===========
% 1.74/1.97
% 1.74/1.97 -------- PROOF --------
% 1.74/1.97
% 1.74/1.97 ----> UNIT CONFLICT at 0.09 sec ----> 1180 [binary,1179.1,1178.1] $F.
% 1.74/1.97
% 1.74/1.97 Length of proof is 33. Level of proof is 16.
% 1.74/1.97
% 1.74/1.97 ---------------- PROOF ----------------
% 1.74/1.97 % SZS status Unsatisfiable
% 1.74/1.97 % SZS output start Refutation
% See solution above
% 1.74/1.97 ------------ end of proof -------------
% 1.74/1.97
% 1.74/1.97
% 1.74/1.97 Search stopped by max_proofs option.
% 1.74/1.97
% 1.74/1.97
% 1.74/1.97 Search stopped by max_proofs option.
% 1.74/1.97
% 1.74/1.97 ============ end of search ============
% 1.74/1.97
% 1.74/1.97 -------------- statistics -------------
% 1.74/1.97 clauses given 35
% 1.74/1.97 clauses generated 2046
% 1.74/1.97 clauses kept 743
% 1.74/1.97 clauses forward subsumed 2093
% 1.74/1.97 clauses back subsumed 9
% 1.74/1.97 Kbytes malloced 1953
% 1.74/1.97
% 1.74/1.97 ----------- times (seconds) -----------
% 1.74/1.97 user CPU time 0.09 (0 hr, 0 min, 0 sec)
% 1.74/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.97 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.97
% 1.74/1.97 That finishes the proof of the theorem.
% 1.74/1.97
% 1.74/1.97 Process 24782 finished Wed Jul 27 03:27:47 2022
% 1.74/1.97 Otter interrupted
% 1.74/1.97 PROOF FOUND
%------------------------------------------------------------------------------