%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : HWC001-1 : TPTP v8.1.0. Bugfixed v1.1.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 12:58:01 EDT 2022
% Result : Unsatisfiable 1.73s 1.92s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 19 ( 18 unt; 0 nHn; 12 RR)
% Number of literals : 21 ( 11 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ output(A,B,C,D)
| ~ output(E,F,G,H)
| output(nand(A,E),nand(B,F),nand(C,G),nand(D,H)) ),
file('HWC001-1.p',unknown),
[] ).
cnf(2,axiom,
~ output(n0,n1,n1,n1),
file('HWC001-1.p',unknown),
[] ).
cnf(4,axiom,
nand(A,B) = not(and(A,B)),
file('HWC001-1.p',unknown),
[] ).
cnf(5,plain,
not(and(A,B)) = nand(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(7,axiom,
and(A,n0) = n0,
file('HWC001-1.p',unknown),
[] ).
cnf(9,axiom,
and(A,n1) = A,
file('HWC001-1.p',unknown),
[] ).
cnf(11,axiom,
not(n0) = n1,
file('HWC001-1.p',unknown),
[] ).
cnf(13,axiom,
not(n1) = n0,
file('HWC001-1.p',unknown),
[] ).
cnf(15,axiom,
output(n0,n0,n1,n1),
file('HWC001-1.p',unknown),
[] ).
cnf(16,axiom,
output(n0,n1,n0,n1),
file('HWC001-1.p',unknown),
[] ).
cnf(18,plain,
not(A) = nand(A,n1),
inference(para_into,[status(thm),theory(equality)],[5,9]),
[iquote('para_into,5.1.1.1,9.1.1')] ).
cnf(19,plain,
nand(n0,n1) = nand(A,n0),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,7]),18]),
[iquote('para_into,5.1.1.1,7.1.1,demod,18')] ).
cnf(21,plain,
nand(n1,n1) = n0,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),18]),
[iquote('back_demod,13,demod,18')] ).
cnf(23,plain,
nand(n0,n1) = n1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),18]),
[iquote('back_demod,11,demod,18')] ).
cnf(27,plain,
nand(A,n0) = n1,
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),23]),
[iquote('copy,19,flip.1,demod,23')] ).
cnf(28,plain,
output(n1,n1,n0,n0),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[15,1,15]),27,27,21,21]),
[iquote('hyper,15,1,15,demod,27,27,21,21')] ).
cnf(29,plain,
output(n1,n0,n1,n0),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[16,1,16]),27,21,27,21]),
[iquote('hyper,16,1,16,demod,27,21,27,21')] ).
cnf(45,plain,
output(n0,n1,n1,n1),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[29,1,28]),21,27,23,27]),
[iquote('hyper,29,1,28,demod,21,27,23,27')] ).
cnf(46,plain,
$false,
inference(binary,[status(thm)],[45,2]),
[iquote('binary,45.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HWC001-1 : TPTP v8.1.0. Bugfixed v1.1.1.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n004.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 04:00:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.73/1.92 ----- Otter 3.3f, August 2004 -----
% 1.73/1.92 The process was started by sandbox2 on n004.cluster.edu,
% 1.73/1.92 Wed Jul 27 04:00:21 2022
% 1.73/1.92 The command was "./otter". The process ID is 7387.
% 1.73/1.92
% 1.73/1.92 set(prolog_style_variables).
% 1.73/1.92 set(auto).
% 1.73/1.92 dependent: set(auto1).
% 1.73/1.92 dependent: set(process_input).
% 1.73/1.92 dependent: clear(print_kept).
% 1.73/1.92 dependent: clear(print_new_demod).
% 1.73/1.92 dependent: clear(print_back_demod).
% 1.73/1.92 dependent: clear(print_back_sub).
% 1.73/1.92 dependent: set(control_memory).
% 1.73/1.92 dependent: assign(max_mem, 12000).
% 1.73/1.92 dependent: assign(pick_given_ratio, 4).
% 1.73/1.92 dependent: assign(stats_level, 1).
% 1.73/1.92 dependent: assign(max_seconds, 10800).
% 1.73/1.92 clear(print_given).
% 1.73/1.92
% 1.73/1.92 list(usable).
% 1.73/1.92 0 [] A=A.
% 1.73/1.92 0 [] nand(X,Y)=not(and(X,Y)).
% 1.73/1.92 0 [] and(X,n0)=n0.
% 1.73/1.92 0 [] and(X,n1)=X.
% 1.73/1.92 0 [] not(n0)=n1.
% 1.73/1.92 0 [] not(n1)=n0.
% 1.73/1.92 0 [] -output(X1,X2,X3,X4)| -output(Y1,Y2,Y3,Y4)|output(nand(X1,Y1),nand(X2,Y2),nand(X3,Y3),nand(X4,Y4)).
% 1.73/1.92 0 [] output(n0,n0,n1,n1).
% 1.73/1.92 0 [] output(n0,n1,n0,n1).
% 1.73/1.92 0 [] -output(n0,n1,n1,n1).
% 1.73/1.92 end_of_list.
% 1.73/1.92
% 1.73/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.73/1.92
% 1.73/1.92 This is a Horn set with equality. The strategy will be
% 1.73/1.92 Knuth-Bendix and hyper_res, with positive clauses in
% 1.73/1.92 sos and nonpositive clauses in usable.
% 1.73/1.92
% 1.73/1.92 dependent: set(knuth_bendix).
% 1.73/1.92 dependent: set(anl_eq).
% 1.73/1.92 dependent: set(para_from).
% 1.73/1.92 dependent: set(para_into).
% 1.73/1.92 dependent: clear(para_from_right).
% 1.73/1.92 dependent: clear(para_into_right).
% 1.73/1.92 dependent: set(para_from_vars).
% 1.73/1.92 dependent: set(eq_units_both_ways).
% 1.73/1.92 dependent: set(dynamic_demod_all).
% 1.73/1.92 dependent: set(dynamic_demod).
% 1.73/1.92 dependent: set(order_eq).
% 1.73/1.92 dependent: set(back_demod).
% 1.73/1.92 dependent: set(lrpo).
% 1.73/1.92 dependent: set(hyper_res).
% 1.73/1.92 dependent: clear(order_hyper).
% 1.73/1.92
% 1.73/1.92 ------------> process usable:
% 1.73/1.92 ** KEPT (pick-wt=23): 1 [] -output(A,B,C,D)| -output(E,F,G,H)|output(nand(A,E),nand(B,F),nand(C,G),nand(D,H)).
% 1.73/1.92 ** KEPT (pick-wt=5): 2 [] -output(n0,n1,n1,n1).
% 1.73/1.92
% 1.73/1.92 ------------> process sos:
% 1.73/1.92 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.73/1.92 ** KEPT (pick-wt=8): 5 [copy,4,flip.1] not(and(A,B))=nand(A,B).
% 1.73/1.92 ---> New Demodulator: 6 [new_demod,5] not(and(A,B))=nand(A,B).
% 1.73/1.92 ** KEPT (pick-wt=5): 7 [] and(A,n0)=n0.
% 1.73/1.92 ---> New Demodulator: 8 [new_demod,7] and(A,n0)=n0.
% 1.73/1.92 ** KEPT (pick-wt=5): 9 [] and(A,n1)=A.
% 1.73/1.92 ---> New Demodulator: 10 [new_demod,9] and(A,n1)=A.
% 1.73/1.92 ** KEPT (pick-wt=4): 11 [] not(n0)=n1.
% 1.73/1.92 ---> New Demodulator: 12 [new_demod,11] not(n0)=n1.
% 1.73/1.92 ** KEPT (pick-wt=4): 13 [] not(n1)=n0.
% 1.73/1.92 ---> New Demodulator: 14 [new_demod,13] not(n1)=n0.
% 1.73/1.92 ** KEPT (pick-wt=5): 15 [] output(n0,n0,n1,n1).
% 1.73/1.92 ** KEPT (pick-wt=5): 16 [] output(n0,n1,n0,n1).
% 1.73/1.92 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.73/1.92 >>>> Starting back demodulation with 6.
% 1.73/1.92 >>>> Starting back demodulation with 8.
% 1.73/1.92 >>>> Starting back demodulation with 10.
% 1.73/1.92 >>>> Starting back demodulation with 12.
% 1.73/1.92 >>>> Starting back demodulation with 14.
% 1.73/1.92
% 1.73/1.92 ======= end of input processing =======
% 1.73/1.92
% 1.73/1.92 =========== start of search ===========
% 1.73/1.92
% 1.73/1.92 -------- PROOF --------
% 1.73/1.92
% 1.73/1.92 ----> UNIT CONFLICT at 0.00 sec ----> 46 [binary,45.1,2.1] $F.
% 1.73/1.92
% 1.73/1.92 Length of proof is 9. Level of proof is 6.
% 1.73/1.92
% 1.73/1.92 ---------------- PROOF ----------------
% 1.73/1.92 % SZS status Unsatisfiable
% 1.73/1.92 % SZS output start Refutation
% See solution above
% 1.73/1.92 ------------ end of proof -------------
% 1.73/1.92
% 1.73/1.92
% 1.73/1.92 Search stopped by max_proofs option.
% 1.73/1.92
% 1.73/1.92
% 1.73/1.92 Search stopped by max_proofs option.
% 1.73/1.92
% 1.73/1.92 ============ end of search ============
% 1.73/1.92
% 1.73/1.92 -------------- statistics -------------
% 1.73/1.92 clauses given 14
% 1.73/1.92 clauses generated 45
% 1.73/1.92 clauses kept 34
% 1.73/1.92 clauses forward subsumed 27
% 1.73/1.92 clauses back subsumed 0
% 1.73/1.92 Kbytes malloced 976
% 1.73/1.92
% 1.73/1.92 ----------- times (seconds) -----------
% 1.73/1.92 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.92 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.73/1.92
% 1.73/1.92 That finishes the proof of the theorem.
% 1.73/1.92
% 1.73/1.92 Process 7387 finished Wed Jul 27 04:00:23 2022
% 1.73/1.92 Otter interrupted
% 1.73/1.92 PROOF FOUND
%------------------------------------------------------------------------------