TSTP Solution File: LCL146-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% 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 13:03:41 EDT 2022
% Result : Unsatisfiable 2.00s 2.18s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of clauses : 53 ( 47 unt; 0 nHn; 11 RR)
% Number of literals : 60 ( 40 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ ordered(A,B)
| implies(A,B) = truth ),
file('LCL146-1.p',unknown),
[] ).
cnf(2,axiom,
( implies(A,B) != truth
| ordered(A,B) ),
file('LCL146-1.p',unknown),
[] ).
cnf(3,axiom,
not(big_hat(x,y)) != big_V(not(x),not(y)),
file('LCL146-1.p',unknown),
[] ).
cnf(4,axiom,
A = A,
file('LCL146-1.p',unknown),
[] ).
cnf(6,axiom,
implies(truth,A) = A,
file('LCL146-1.p',unknown),
[] ).
cnf(7,axiom,
implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth,
file('LCL146-1.p',unknown),
[] ).
cnf(9,axiom,
implies(implies(A,B),B) = implies(implies(B,A),A),
file('LCL146-1.p',unknown),
[] ).
cnf(10,axiom,
implies(implies(not(A),not(B)),implies(B,A)) = truth,
file('LCL146-1.p',unknown),
[] ).
cnf(12,axiom,
big_V(A,B) = implies(implies(A,B),B),
file('LCL146-1.p',unknown),
[] ).
cnf(14,plain,
implies(implies(A,B),B) = big_V(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.1')] ).
cnf(15,axiom,
big_hat(A,B) = not(big_V(not(A),not(B))),
file('LCL146-1.p',unknown),
[] ).
cnf(16,plain,
not(big_V(not(A),not(B))) = big_hat(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(18,plain,
big_V(A,B) = big_V(B,A),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),14,14]),
[iquote('copy,9,flip.1,demod,14,14')] ).
cnf(22,plain,
( ~ ordered(truth,A)
| A = truth ),
inference(para_from,[status(thm),theory(equality)],[6,1]),
[iquote('para_from,5.1.1,1.2.1')] ).
cnf(28,plain,
ordered(implies(A,B),implies(implies(B,C),implies(A,C))),
inference(hyper,[status(thm)],[7,2]),
[iquote('hyper,7,2')] ).
cnf(31,plain,
implies(A,big_V(A,B)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,6]),6,14]),
[iquote('para_into,7.1.1.1,5.1.1,demod,6,14')] ).
cnf(36,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(para_into,[status(thm),theory(equality)],[7,6]),
[iquote('para_into,7.1.1.2.1,5.1.1')] ).
cnf(54,plain,
( truth != truth
| ordered(A,B)
| ~ ordered(truth,implies(A,B)) ),
inference(para_from,[status(thm),theory(equality)],[22,2]),
[iquote('para_from,22.2.1,2.1.1')] ).
cnf(58,plain,
ordered(A,big_V(A,B)),
inference(hyper,[status(thm)],[31,2]),
[iquote('hyper,31,2')] ).
cnf(63,plain,
big_V(truth,A) = truth,
inference(para_into,[status(thm),theory(equality)],[31,6]),
[iquote('para_into,31.1.1,5.1.1')] ).
cnf(70,plain,
ordered(implies(not(A),not(B)),implies(B,A)),
inference(hyper,[status(thm)],[10,2]),
[iquote('hyper,10,2')] ).
cnf(82,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(para_into,[status(thm),theory(equality)],[10,6]),
[iquote('para_into,10.1.1.2,5.1.1')] ).
cnf(91,plain,
implies(implies(implies(A,B),C),implies(implies(not(B),not(A)),C)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[10,7]),6]),
[iquote('para_from,10.1.1,7.1.1.1,demod,6')] ).
cnf(94,plain,
ordered(A,big_V(B,A)),
inference(para_into,[status(thm),theory(equality)],[58,18]),
[iquote('para_into,58.1.2,18.1.1')] ).
cnf(98,plain,
ordered(A,truth),
inference(para_into,[status(thm),theory(equality)],[94,63]),
[iquote('para_into,94.1.2,62.1.1')] ).
cnf(100,plain,
implies(A,truth) = truth,
inference(hyper,[status(thm)],[98,1]),
[iquote('hyper,98,1')] ).
cnf(102,plain,
implies(A,implies(B,A)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[36]),100,6]),
[iquote('back_demod,36,demod,100,6')] ).
cnf(114,plain,
implies(A,A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,6]),63]),
[iquote('para_into,13.1.1.1,5.1.1,demod,63')] ).
cnf(116,plain,
( big_V(A,B) = B
| ~ ordered(A,B) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,1]),6])]),
[iquote('para_into,13.1.1.1,1.2.1,demod,6,flip.1')] ).
cnf(130,plain,
big_V(A,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[114,14]),6])]),
[iquote('para_from,114.1.1,13.1.1.1,demod,6,flip.1')] ).
cnf(142,plain,
implies(implies(big_hat(A,B),not(C)),implies(C,big_V(not(A),not(B)))) = truth,
inference(para_from,[status(thm),theory(equality)],[16,10]),
[iquote('para_from,16.1.1,10.1.1.1.1')] ).
cnf(145,plain,
not(not(A)) = big_hat(A,A),
inference(para_from,[status(thm),theory(equality)],[130,16]),
[iquote('para_from,130.1.1,16.1.1.1')] ).
cnf(187,plain,
not(big_hat(A,B)) = big_hat(big_V(not(A),not(B)),big_V(not(A),not(B))),
inference(para_into,[status(thm),theory(equality)],[145,16]),
[iquote('para_into,144.1.1.1,16.1.1')] ).
cnf(195,plain,
big_hat(big_V(not(x),not(y)),big_V(not(x),not(y))) != big_V(not(x),not(y)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),187]),
[iquote('back_demod,3,demod,187')] ).
cnf(222,plain,
( big_V(A,B) = A
| ~ ordered(B,A) ),
inference(para_into,[status(thm),theory(equality)],[116,18]),
[iquote('para_into,116.1.1,18.1.1')] ).
cnf(275,plain,
ordered(implies(A,B),implies(A,implies(C,B))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,102]),6]),
[iquote('para_into,28.1.2.1,102.1.1,demod,6')] ).
cnf(306,plain,
ordered(implies(not(A),not(truth)),A),
inference(para_into,[status(thm),theory(equality)],[70,6]),
[iquote('para_into,70.1.2,5.1.1')] ).
cnf(307,plain,
big_V(A,implies(not(A),not(truth))) = A,
inference(hyper,[status(thm)],[306,222]),
[iquote('hyper,306,222')] ).
cnf(415,plain,
big_V(big_hat(truth,truth),not(truth)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[82,14]),145]),
[iquote('para_into,82.1.1,13.1.1,demod,145')] ).
cnf(1105,plain,
ordered(truth,implies(A,implies(B,implies(C,A)))),
inference(para_into,[status(thm),theory(equality)],[275,102]),
[iquote('para_into,275.1.1,102.1.1')] ).
cnf(1324,plain,
ordered(A,implies(B,implies(C,A))),
inference(hyper,[status(thm)],[1105,54,4]),
[iquote('hyper,1105,54,4')] ).
cnf(1334,plain,
ordered(A,big_V(B,implies(C,A))),
inference(para_into,[status(thm),theory(equality)],[1324,14]),
[iquote('para_into,1324.1.2,13.1.1')] ).
cnf(1344,plain,
ordered(not(truth),A),
inference(para_into,[status(thm),theory(equality)],[1334,307]),
[iquote('para_into,1334.1.2,307.1.1')] ).
cnf(1348,plain,
big_V(A,not(truth)) = A,
inference(hyper,[status(thm)],[1344,222]),
[iquote('hyper,1344,222')] ).
cnf(1367,plain,
big_hat(truth,truth) = truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[415]),1348]),
[iquote('back_demod,415,demod,1348')] ).
cnf(1378,plain,
big_hat(A,A) = big_hat(A,truth),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1348,16]),145]),
[iquote('para_from,1347.1.1,16.1.1.1,demod,145')] ).
cnf(1417,plain,
implies(big_hat(A,A),A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[91,82]),145,1367,145,6,6]),
[iquote('para_into,91.1.1.1,82.1.1,demod,145,1367,145,6,6')] ).
cnf(1419,plain,
ordered(big_hat(A,A),A),
inference(hyper,[status(thm)],[1417,2]),
[iquote('hyper,1417,2')] ).
cnf(1422,plain,
implies(big_hat(A,truth),A) = truth,
inference(para_into,[status(thm),theory(equality)],[1417,1378]),
[iquote('para_into,1417.1.1.1,1378.1.1')] ).
cnf(1437,plain,
big_V(A,big_hat(A,A)) = A,
inference(hyper,[status(thm)],[1419,222]),
[iquote('hyper,1419,222')] ).
cnf(1698,plain,
implies(A,big_hat(A,A)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[142,1422]),145,1348,6]),
[iquote('para_into,142.1.1.1,1422.1.1,demod,145,1348,6')] ).
cnf(1714,plain,
big_hat(A,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1698,14]),6,1437]),
[iquote('para_from,1698.1.1,13.1.1.1,demod,6,1437')] ).
cnf(1716,plain,
$false,
inference(binary,[status(thm)],[1714,195]),
[iquote('binary,1714.1,195.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n007.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 09:06:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.00/2.17 ----- Otter 3.3f, August 2004 -----
% 2.00/2.17 The process was started by sandbox2 on n007.cluster.edu,
% 2.00/2.17 Wed Jul 27 09:06:01 2022
% 2.00/2.17 The command was "./otter". The process ID is 10469.
% 2.00/2.17
% 2.00/2.17 set(prolog_style_variables).
% 2.00/2.17 set(auto).
% 2.00/2.17 dependent: set(auto1).
% 2.00/2.17 dependent: set(process_input).
% 2.00/2.17 dependent: clear(print_kept).
% 2.00/2.17 dependent: clear(print_new_demod).
% 2.00/2.17 dependent: clear(print_back_demod).
% 2.00/2.17 dependent: clear(print_back_sub).
% 2.00/2.17 dependent: set(control_memory).
% 2.00/2.17 dependent: assign(max_mem, 12000).
% 2.00/2.17 dependent: assign(pick_given_ratio, 4).
% 2.00/2.17 dependent: assign(stats_level, 1).
% 2.00/2.17 dependent: assign(max_seconds, 10800).
% 2.00/2.17 clear(print_given).
% 2.00/2.17
% 2.00/2.17 list(usable).
% 2.00/2.17 0 [] A=A.
% 2.00/2.17 0 [] implies(truth,X)=X.
% 2.00/2.17 0 [] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))=truth.
% 2.00/2.17 0 [] implies(implies(X,Y),Y)=implies(implies(Y,X),X).
% 2.00/2.17 0 [] implies(implies(not(X),not(Y)),implies(Y,X))=truth.
% 2.00/2.17 0 [] big_V(X,Y)=implies(implies(X,Y),Y).
% 2.00/2.17 0 [] big_hat(X,Y)=not(big_V(not(X),not(Y))).
% 2.00/2.17 0 [] -ordered(X,Y)|implies(X,Y)=truth.
% 2.00/2.17 0 [] implies(X,Y)!=truth|ordered(X,Y).
% 2.00/2.17 0 [] not(big_hat(x,y))!=big_V(not(x),not(y)).
% 2.00/2.17 end_of_list.
% 2.00/2.17
% 2.00/2.17 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 2.00/2.17
% 2.00/2.17 This is a Horn set with equality. The strategy will be
% 2.00/2.17 Knuth-Bendix and hyper_res, with positive clauses in
% 2.00/2.17 sos and nonpositive clauses in usable.
% 2.00/2.17
% 2.00/2.17 dependent: set(knuth_bendix).
% 2.00/2.17 dependent: set(anl_eq).
% 2.00/2.17 dependent: set(para_from).
% 2.00/2.17 dependent: set(para_into).
% 2.00/2.17 dependent: clear(para_from_right).
% 2.00/2.17 dependent: clear(para_into_right).
% 2.00/2.17 dependent: set(para_from_vars).
% 2.00/2.17 dependent: set(eq_units_both_ways).
% 2.00/2.17 dependent: set(dynamic_demod_all).
% 2.00/2.17 dependent: set(dynamic_demod).
% 2.00/2.17 dependent: set(order_eq).
% 2.00/2.17 dependent: set(back_demod).
% 2.00/2.17 dependent: set(lrpo).
% 2.00/2.17 dependent: set(hyper_res).
% 2.00/2.17 dependent: clear(order_hyper).
% 2.00/2.17
% 2.00/2.17 ------------> process usable:
% 2.00/2.17 ** KEPT (pick-wt=8): 1 [] -ordered(A,B)|implies(A,B)=truth.
% 2.00/2.17 ** KEPT (pick-wt=8): 2 [] implies(A,B)!=truth|ordered(A,B).
% 2.00/2.17 ** KEPT (pick-wt=10): 3 [] not(big_hat(x,y))!=big_V(not(x),not(y)).
% 2.00/2.17
% 2.00/2.17 ------------> process sos:
% 2.00/2.17 ** KEPT (pick-wt=3): 4 [] A=A.
% 2.00/2.17 ** KEPT (pick-wt=5): 5 [] implies(truth,A)=A.
% 2.00/2.17 ---> New Demodulator: 6 [new_demod,5] implies(truth,A)=A.
% 2.00/2.17 ** KEPT (pick-wt=13): 7 [] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 2.00/2.17 ---> New Demodulator: 8 [new_demod,7] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 2.00/2.17 ** KEPT (pick-wt=11): 9 [] implies(implies(A,B),B)=implies(implies(B,A),A).
% 2.00/2.17 ** KEPT (pick-wt=11): 10 [] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 2.00/2.17 ---> New Demodulator: 11 [new_demod,10] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 2.00/2.17 ** KEPT (pick-wt=9): 13 [copy,12,flip.1] implies(implies(A,B),B)=big_V(A,B).
% 2.00/2.17 ---> New Demodulator: 14 [new_demod,13] implies(implies(A,B),B)=big_V(A,B).
% 2.00/2.17 ** KEPT (pick-wt=10): 16 [copy,15,flip.1] not(big_V(not(A),not(B)))=big_hat(A,B).
% 2.00/2.17 ---> New Demodulator: 17 [new_demod,16] not(big_V(not(A),not(B)))=big_hat(A,B).
% 2.00/2.17 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 2.00/2.17 >>>> Starting back demodulation with 6.
% 2.00/2.17 >>>> Starting back demodulation with 8.
% 2.00/2.18 ** KEPT (pick-wt=7): 18 [copy,9,flip.1,demod,14,14] big_V(A,B)=big_V(B,A).
% 2.00/2.18 >>>> Starting back demodulation with 11.
% 2.00/2.18 >>>> Starting back demodulation with 14.
% 2.00/2.18 >> back demodulating 9 with 14.
% 2.00/2.18 >>>> Starting back demodulation with 17.
% 2.00/2.18 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] big_V(A,B)=big_V(B,A).
% 2.00/2.18
% 2.00/2.18 ======= end of input processing =======
% 2.00/2.18
% 2.00/2.18 =========== start of search ===========
% 2.00/2.18
% 2.00/2.18
% 2.00/2.18 Resetting weight limit to 10.
% 2.00/2.18
% 2.00/2.18
% 2.00/2.18 Resetting weight limit to 10.
% 2.00/2.18
% 2.00/2.18 sos_size=966
% 2.00/2.18
% 2.00/2.18
% 2.00/2.18 Resetting weight limit to 9.
% 2.00/2.18
% 2.00/2.18
% 2.00/2.18 Resetting weight limit to 9.
% 2.00/2.18
% 2.00/2.18 sos_size=950
% 2.00/2.18
% 2.00/2.18 -------- PROOF --------
% 2.00/2.18
% 2.00/2.18 ----> UNIT CONFLICT at 0.25 sec ----> 1716 [binary,1714.1,195.1] $F.
% 2.00/2.18
% 2.00/2.18 Length of proof is 42. Level of proof is 18.
% 2.00/2.18
% 2.00/2.18 ---------------- PROOF ----------------
% 2.00/2.18 % SZS status Unsatisfiable
% 2.00/2.18 % SZS output start Refutation
% See solution above
% 2.00/2.18 ------------ end of proof -------------
% 2.00/2.18
% 2.00/2.18
% 2.00/2.18 Search stopped by max_proofs option.
% 2.00/2.18
% 2.00/2.18
% 2.00/2.18 Search stopped by max_proofs option.
% 2.00/2.18
% 2.00/2.18 ============ end of search ============
% 2.00/2.18
% 2.00/2.18 -------------- statistics -------------
% 2.00/2.18 clauses given 202
% 2.00/2.18 clauses generated 18226
% 2.00/2.18 clauses kept 1505
% 2.00/2.18 clauses forward subsumed 9550
% 2.00/2.18 clauses back subsumed 129
% 2.00/2.18 Kbytes malloced 5859
% 2.00/2.18
% 2.00/2.18 ----------- times (seconds) -----------
% 2.00/2.18 user CPU time 0.25 (0 hr, 0 min, 0 sec)
% 2.00/2.18 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.18 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.00/2.18
% 2.00/2.18 That finishes the proof of the theorem.
% 2.00/2.18
% 2.00/2.18 Process 10469 finished Wed Jul 27 09:06:03 2022
% 2.00/2.18 Otter interrupted
% 2.00/2.18 PROOF FOUND
%------------------------------------------------------------------------------