TSTP Solution File: LAT394-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT394-2 : TPTP v8.1.0. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:03:15 EDT 2022
% Result : Unsatisfiable 1.91s 2.12s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 3 RR)
% Number of literals : 34 ( 33 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
f(x0,f(x0,x0)) != f(x1,f(x1,x1)),
file('LAT394-2.p',unknown),
[] ).
cnf(2,plain,
f(x1,f(x1,x1)) != f(x0,f(x0,x0)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(5,axiom,
f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C))) = B,
file('LAT394-2.p',unknown),
[] ).
cnf(8,plain,
f(f(f(f(A,f(f(f(B,C),f(C,D)),E)),C),F),f(f(f(f(B,C),f(C,D)),E),f(f(f(f(f(B,C),f(C,D)),E),f(f(A,A),A)),f(C,f(f(C,f(f(B,B),B)),D))))) = f(f(f(B,C),f(C,D)),E),
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.1.1.2,4.1.1')] ).
cnf(13,plain,
f(A,f(f(A,B),f(f(f(A,B),f(f(f(C,A),f(C,A)),f(C,A))),D))) = f(A,B),
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.1,4.1.1')] ).
cnf(22,plain,
f(f(A,B),f(f(f(A,B),f(B,C)),B)) = f(f(A,B),f(B,C)),
inference(para_into,[status(thm),theory(equality)],[13,5]),
[iquote('para_into,12.1.1.2.2,4.1.1')] ).
cnf(26,plain,
f(f(f(f(A,B),f(B,f(f(f(B,f(f(A,A),A)),f(f(f(C,B),f(C,B)),f(C,B))),D))),E),f(B,f(f(A,A),A))) = B,
inference(para_from,[status(thm),theory(equality)],[13,5]),
[iquote('para_from,12.1.1,4.1.1.2')] ).
cnf(43,plain,
f(f(f(f(A,B),f(B,C)),B),f(B,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,5]),5]),
[iquote('para_into,22.1.1.2.1,4.1.1,demod,5')] ).
cnf(66,plain,
f(f(A,A),f(A,A)) = A,
inference(para_into,[status(thm),theory(equality)],[43,43]),
[iquote('para_into,42.1.1.1.1,42.1.1')] ).
cnf(78,plain,
f(A,f(f(A,f(f(A,A),B)),f(A,A))) = f(A,f(f(A,A),B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[43,22]),43,43]),
[iquote('para_from,42.1.1,22.1.1.1,demod,43,43')] ).
cnf(167,plain,
f(f(A,B),f(A,f(f(A,f(f(A,A),A)),A))) = A,
inference(para_from,[status(thm),theory(equality)],[66,5]),
[iquote('para_from,66.1.1,4.1.1.1.1')] ).
cnf(180,plain,
f(A,f(f(A,B),f(A,B))) = f(A,B),
inference(para_from,[status(thm),theory(equality)],[167,13]),
[iquote('para_from,166.1.1,12.1.1.2.2')] ).
cnf(185,plain,
f(A,f(f(A,f(f(A,A),A)),A)) = f(A,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[167,66]),167])]),
[iquote('para_from,166.1.1,66.1.1.2,demod,167,flip.1')] ).
cnf(195,plain,
f(f(A,B),f(A,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[167]),185]),
[iquote('back_demod,166,demod,185')] ).
cnf(197,plain,
f(A,f(f(A,A),B)) = f(A,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[78]),195])]),
[iquote('back_demod,78,demod,195,flip.1')] ).
cnf(201,plain,
f(f(f(A,A),B),A) = f(A,A),
inference(para_into,[status(thm),theory(equality)],[195,195]),
[iquote('para_into,194.1.1.2,194.1.1')] ).
cnf(207,plain,
f(f(A,A),f(A,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[197,195]),195]),
[iquote('para_into,196.1.1.2.1,194.1.1,demod,195')] ).
cnf(218,plain,
f(f(f(A,B),f(A,B)),A) = f(A,B),
inference(para_into,[status(thm),theory(equality)],[207,195]),
[iquote('para_into,206.1.1.2,194.1.1')] ).
cnf(244,plain,
f(f(f(f(A,B),f(B,C)),D),f(B,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[180,5]),5,5]),
[iquote('para_into,180.1.1.2.1,4.1.1,demod,5,5')] ).
cnf(271,plain,
f(f(A,B),f(B,B)) = B,
inference(para_into,[status(thm),theory(equality)],[244,195]),
[iquote('para_into,244.1.1.1,194.1.1')] ).
cnf(287,plain,
f(A,f(f(B,A),f(B,A))) = f(B,A),
inference(para_from,[status(thm),theory(equality)],[271,195]),
[iquote('para_from,270.1.1,194.1.1.1')] ).
cnf(289,plain,
f(f(A,A),f(B,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[271,218]),271,271]),
[iquote('para_from,270.1.1,218.1.1.1.2,demod,271,271')] ).
cnf(290,plain,
f(A,f(B,f(A,A))) = f(A,A),
inference(para_into,[status(thm),theory(equality)],[289,289]),
[iquote('para_into,288.1.1.1,288.1.1')] ).
cnf(361,plain,
f(f(A,B),f(A,f(f(C,C),C))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,290]),271]),
[iquote('para_into,26.1.1.1.1.2,290.1.1,demod,271')] ).
cnf(365,plain,
f(f(f(f(A,A),A),f(f(A,A),A)),B) = f(f(A,A),A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[26,8]),287,197,197,207,287,197,13,289,201,195,287,197])]),
[iquote('para_from,26.1.1,8.1.1.2.2.1,demod,287,197,197,207,287,197,13,289,201,195,287,197,flip.1')] ).
cnf(366,plain,
f(A,A) = f(A,f(f(B,B),B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[26,289]),361]),
[iquote('para_from,26.1.1,288.1.1.2,demod,361')] ).
cnf(371,plain,
f(f(A,A),f(f(B,B),B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[366,289])]),
[iquote('para_into,366.1.1,288.1.1,flip.1')] ).
cnf(385,plain,
f(f(A,f(f(B,B),B)),f(C,A)) = A,
inference(para_from,[status(thm),theory(equality)],[366,289]),
[iquote('para_from,366.1.1,288.1.1.1')] ).
cnf(407,plain,
f(f(A,A),f(B,f(B,B))) = A,
inference(para_into,[status(thm),theory(equality)],[371,289]),
[iquote('para_into,371.1.1.2.1,288.1.1')] ).
cnf(460,plain,
f(f(A,f(A,A)),f(B,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[407,287]),407,407]),
[iquote('para_from,406.1.1,286.1.1.2.2,demod,407,407')] ).
cnf(480,plain,
f(f(A,f(A,A)),B) = f(B,B),
inference(para_into,[status(thm),theory(equality)],[460,289]),
[iquote('para_into,460.1.1.2,288.1.1')] ).
cnf(602,plain,
f(f(A,A),A) = f(B,f(B,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[385,480]),365]),
[iquote('para_into,385.1.1.1,480.1.1,demod,365')] ).
cnf(606,plain,
f(A,f(A,A)) = f(B,f(B,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[602,480]),407]),
[iquote('para_into,602.1.1.1,480.1.1,demod,407')] ).
cnf(607,plain,
$false,
inference(binary,[status(thm)],[606,2]),
[iquote('binary,606.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT394-2 : TPTP v8.1.0. Released v5.4.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 08:26:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.91/2.12 ----- Otter 3.3f, August 2004 -----
% 1.91/2.12 The process was started by sandbox on n012.cluster.edu,
% 1.91/2.12 Wed Jul 27 08:26:05 2022
% 1.91/2.12 The command was "./otter". The process ID is 16346.
% 1.91/2.12
% 1.91/2.12 set(prolog_style_variables).
% 1.91/2.12 set(auto).
% 1.91/2.12 dependent: set(auto1).
% 1.91/2.12 dependent: set(process_input).
% 1.91/2.12 dependent: clear(print_kept).
% 1.91/2.12 dependent: clear(print_new_demod).
% 1.91/2.12 dependent: clear(print_back_demod).
% 1.91/2.12 dependent: clear(print_back_sub).
% 1.91/2.12 dependent: set(control_memory).
% 1.91/2.12 dependent: assign(max_mem, 12000).
% 1.91/2.12 dependent: assign(pick_given_ratio, 4).
% 1.91/2.12 dependent: assign(stats_level, 1).
% 1.91/2.12 dependent: assign(max_seconds, 10800).
% 1.91/2.12 clear(print_given).
% 1.91/2.12
% 1.91/2.12 list(usable).
% 1.91/2.12 0 [] A=A.
% 1.91/2.12 0 [] f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C)))=B.
% 1.91/2.12 0 [] f(x0,f(x0,x0))!=f(x1,f(x1,x1)).
% 1.91/2.12 end_of_list.
% 1.91/2.12
% 1.91/2.12 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.91/2.12
% 1.91/2.12 All clauses are units, and equality is present; the
% 1.91/2.12 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.91/2.12
% 1.91/2.12 dependent: set(knuth_bendix).
% 1.91/2.12 dependent: set(anl_eq).
% 1.91/2.12 dependent: set(para_from).
% 1.91/2.12 dependent: set(para_into).
% 1.91/2.12 dependent: clear(para_from_right).
% 1.91/2.12 dependent: clear(para_into_right).
% 1.91/2.12 dependent: set(para_from_vars).
% 1.91/2.12 dependent: set(eq_units_both_ways).
% 1.91/2.12 dependent: set(dynamic_demod_all).
% 1.91/2.12 dependent: set(dynamic_demod).
% 1.91/2.12 dependent: set(order_eq).
% 1.91/2.12 dependent: set(back_demod).
% 1.91/2.12 dependent: set(lrpo).
% 1.91/2.12
% 1.91/2.12 ------------> process usable:
% 1.91/2.12 ** KEPT (pick-wt=11): 2 [copy,1,flip.1] f(x1,f(x1,x1))!=f(x0,f(x0,x0)).
% 1.91/2.12
% 1.91/2.12 ------------> process sos:
% 1.91/2.12 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.91/2.12 ** KEPT (pick-wt=23): 4 [] f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C)))=B.
% 1.91/2.12 ---> New Demodulator: 5 [new_demod,4] f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C)))=B.
% 1.91/2.12 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.91/2.12 >>>> Starting back demodulation with 5.
% 1.91/2.12
% 1.91/2.12 ======= end of input processing =======
% 1.91/2.12
% 1.91/2.12 =========== start of search ===========
% 1.91/2.12
% 1.91/2.12
% 1.91/2.12 Resetting weight limit to 29.
% 1.91/2.12
% 1.91/2.12
% 1.91/2.12 Resetting weight limit to 29.
% 1.91/2.12
% 1.91/2.12 sos_size=66
% 1.91/2.12
% 1.91/2.12
% 1.91/2.12 Resetting weight limit to 15.
% 1.91/2.12
% 1.91/2.12
% 1.91/2.12 Resetting weight limit to 15.
% 1.91/2.12
% 1.91/2.12 sos_size=87
% 1.91/2.12
% 1.91/2.12 -------- PROOF --------
% 1.91/2.12
% 1.91/2.12 ----> UNIT CONFLICT at 0.22 sec ----> 607 [binary,606.1,2.1] $F.
% 1.91/2.12
% 1.91/2.12 Length of proof is 31. Level of proof is 20.
% 1.91/2.12
% 1.91/2.12 ---------------- PROOF ----------------
% 1.91/2.12 % SZS status Unsatisfiable
% 1.91/2.12 % SZS output start Refutation
% See solution above
% 1.91/2.12 ------------ end of proof -------------
% 1.91/2.12
% 1.91/2.12
% 1.91/2.12 Search stopped by max_proofs option.
% 1.91/2.12
% 1.91/2.12
% 1.91/2.12 Search stopped by max_proofs option.
% 1.91/2.12
% 1.91/2.12 ============ end of search ============
% 1.91/2.12
% 1.91/2.12 -------------- statistics -------------
% 1.91/2.12 clauses given 45
% 1.91/2.12 clauses generated 4573
% 1.91/2.12 clauses kept 338
% 1.91/2.12 clauses forward subsumed 2553
% 1.91/2.12 clauses back subsumed 4
% 1.91/2.12 Kbytes malloced 4882
% 1.91/2.12
% 1.91/2.12 ----------- times (seconds) -----------
% 1.91/2.12 user CPU time 0.22 (0 hr, 0 min, 0 sec)
% 1.91/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.91/2.12
% 1.91/2.12 That finishes the proof of the theorem.
% 1.91/2.12
% 1.91/2.12 Process 16346 finished Wed Jul 27 08:26:07 2022
% 1.91/2.12 Otter interrupted
% 1.91/2.12 PROOF FOUND
%------------------------------------------------------------------------------