TSTP Solution File: LCL301-3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL301-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:04:10 EDT 2022
% Result : Unsatisfiable 1.69s 1.87s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 33 unt; 0 nHn; 5 RR)
% Number of literals : 38 ( 6 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( theorem(A)
| ~ axiom(A) ),
file('LCL301-3.p',unknown),
[] ).
cnf(2,axiom,
( theorem(A)
| ~ theorem(implies(B,A))
| ~ theorem(B) ),
file('LCL301-3.p',unknown),
[] ).
cnf(3,axiom,
~ theorem(e_quivalent(not(implies(not(p),not(q))),and(not(p),q))),
file('LCL301-3.p',unknown),
[] ).
cnf(5,axiom,
axiom(implies(or(A,A),A)),
file('LCL301-3.p',unknown),
[] ).
cnf(6,axiom,
axiom(implies(A,or(B,A))),
file('LCL301-3.p',unknown),
[] ).
cnf(7,axiom,
axiom(implies(or(A,B),or(B,A))),
file('LCL301-3.p',unknown),
[] ).
cnf(8,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('LCL301-3.p',unknown),
[] ).
cnf(10,axiom,
implies(A,B) = or(not(A),B),
file('LCL301-3.p',unknown),
[] ).
cnf(12,plain,
or(not(A),B) = implies(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(13,axiom,
and(A,B) = not(or(not(A),not(B))),
file('LCL301-3.p',unknown),
[] ).
cnf(15,plain,
not(implies(A,not(B))) = and(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13]),12])]),
[iquote('copy,13,demod,12,flip.1')] ).
cnf(16,axiom,
e_quivalent(A,B) = and(implies(A,B),implies(B,A)),
file('LCL301-3.p',unknown),
[] ).
cnf(17,plain,
and(implies(A,B),implies(B,A)) = e_quivalent(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[16])]),
[iquote('copy,16,flip.1')] ).
cnf(19,plain,
~ theorem(e_quivalent(and(not(p),q),and(not(p),q))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),15]),
[iquote('back_demod,3,demod,15')] ).
cnf(20,plain,
theorem(implies(or(A,A),A)),
inference(hyper,[status(thm)],[5,1]),
[iquote('hyper,5,1')] ).
cnf(21,plain,
theorem(implies(A,or(B,A))),
inference(hyper,[status(thm)],[6,1]),
[iquote('hyper,6,1')] ).
cnf(24,plain,
theorem(implies(or(A,B),or(B,A))),
inference(hyper,[status(thm)],[7,1]),
[iquote('hyper,7,1')] ).
cnf(29,plain,
theorem(implies(implies(A,not(A)),not(A))),
inference(para_from,[status(thm),theory(equality)],[12,20]),
[iquote('para_from,11.1.1,20.1.1.1')] ).
cnf(37,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(hyper,[status(thm)],[8,1]),
[iquote('hyper,8,1')] ).
cnf(47,plain,
theorem(implies(implies(A,B),or(B,not(A)))),
inference(para_into,[status(thm),theory(equality)],[24,12]),
[iquote('para_into,24.1.1.1,11.1.1')] ).
cnf(48,plain,
theorem(implies(or(A,not(B)),implies(B,A))),
inference(para_into,[status(thm),theory(equality)],[24,12]),
[iquote('para_into,24.1.1.2,11.1.1')] ).
cnf(80,plain,
theorem(implies(A,and(A,A))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[47,2,29]),15,12]),
[iquote('hyper,47,2,29,demod,15,12')] ).
cnf(83,plain,
theorem(or(or(A,B),not(B))),
inference(hyper,[status(thm)],[47,2,21]),
[iquote('hyper,47,2,21')] ).
cnf(106,plain,
theorem(implies(implies(A,A),e_quivalent(A,A))),
inference(para_into,[status(thm),theory(equality)],[80,17]),
[iquote('para_into,80.1.1.2,17.1.1')] ).
cnf(113,plain,
theorem(or(A,or(or(B,C),not(C)))),
inference(hyper,[status(thm)],[83,2,21]),
[iquote('hyper,83,2,21')] ).
cnf(190,plain,
theorem(or(or(A,B),or(C,not(B)))),
inference(hyper,[status(thm)],[113,2,37]),
[iquote('hyper,113,2,37')] ).
cnf(228,plain,
theorem(or(or(A,not(B)),or(C,B))),
inference(hyper,[status(thm)],[190,2,24]),
[iquote('hyper,190,2,24')] ).
cnf(246,plain,
theorem(or(A,or(or(B,not(C)),C))),
inference(hyper,[status(thm)],[228,2,37]),
[iquote('hyper,228,2,37')] ).
cnf(252,plain,
theorem(or(or(A,not(B)),B)),
inference(hyper,[status(thm)],[246,2,20]),
[iquote('hyper,246,2,20')] ).
cnf(256,plain,
theorem(or(A,or(B,not(A)))),
inference(hyper,[status(thm)],[252,2,24]),
[iquote('hyper,252,2,24')] ).
cnf(258,plain,
theorem(or(A,or(B,not(B)))),
inference(hyper,[status(thm)],[256,2,37]),
[iquote('hyper,256,2,37')] ).
cnf(267,plain,
theorem(or(A,not(A))),
inference(hyper,[status(thm)],[258,2,20]),
[iquote('hyper,258,2,20')] ).
cnf(271,plain,
theorem(implies(A,A)),
inference(hyper,[status(thm)],[267,2,48]),
[iquote('hyper,267,2,48')] ).
cnf(276,plain,
theorem(e_quivalent(A,A)),
inference(hyper,[status(thm)],[271,2,106]),
[iquote('hyper,271,2,106')] ).
cnf(277,plain,
$false,
inference(binary,[status(thm)],[276,19]),
[iquote('binary,276.1,19.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL301-3 : TPTP v8.1.0. Released v2.3.0.
% 0.13/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n027.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 09:42:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.69/1.87 ----- Otter 3.3f, August 2004 -----
% 1.69/1.87 The process was started by sandbox on n027.cluster.edu,
% 1.69/1.87 Wed Jul 27 09:42:52 2022
% 1.69/1.87 The command was "./otter". The process ID is 30378.
% 1.69/1.87
% 1.69/1.87 set(prolog_style_variables).
% 1.69/1.87 set(auto).
% 1.69/1.87 dependent: set(auto1).
% 1.69/1.87 dependent: set(process_input).
% 1.69/1.87 dependent: clear(print_kept).
% 1.69/1.87 dependent: clear(print_new_demod).
% 1.69/1.87 dependent: clear(print_back_demod).
% 1.69/1.87 dependent: clear(print_back_sub).
% 1.69/1.87 dependent: set(control_memory).
% 1.69/1.87 dependent: assign(max_mem, 12000).
% 1.69/1.87 dependent: assign(pick_given_ratio, 4).
% 1.69/1.87 dependent: assign(stats_level, 1).
% 1.69/1.87 dependent: assign(max_seconds, 10800).
% 1.69/1.87 clear(print_given).
% 1.69/1.87
% 1.69/1.87 list(usable).
% 1.69/1.87 0 [] A=A.
% 1.69/1.87 0 [] axiom(implies(or(A,A),A)).
% 1.69/1.87 0 [] axiom(implies(A,or(B,A))).
% 1.69/1.87 0 [] axiom(implies(or(A,B),or(B,A))).
% 1.69/1.87 0 [] axiom(implies(or(A,or(B,C)),or(B,or(A,C)))).
% 1.69/1.87 0 [] axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))).
% 1.69/1.87 0 [] implies(X,Y)=or(not(X),Y).
% 1.69/1.87 0 [] theorem(X)| -axiom(X).
% 1.69/1.87 0 [] theorem(X)| -theorem(implies(Y,X))| -theorem(Y).
% 1.69/1.87 0 [] and(P,Q)=not(or(not(P),not(Q))).
% 1.69/1.87 0 [] e_quivalent(P,Q)=and(implies(P,Q),implies(Q,P)).
% 1.69/1.87 0 [] -theorem(e_quivalent(not(implies(not(p),not(q))),and(not(p),q))).
% 1.69/1.87 end_of_list.
% 1.69/1.87
% 1.69/1.87 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.69/1.87
% 1.69/1.87 This is a Horn set with equality. The strategy will be
% 1.69/1.87 Knuth-Bendix and hyper_res, with positive clauses in
% 1.69/1.87 sos and nonpositive clauses in usable.
% 1.69/1.87
% 1.69/1.87 dependent: set(knuth_bendix).
% 1.69/1.87 dependent: set(anl_eq).
% 1.69/1.87 dependent: set(para_from).
% 1.69/1.87 dependent: set(para_into).
% 1.69/1.87 dependent: clear(para_from_right).
% 1.69/1.87 dependent: clear(para_into_right).
% 1.69/1.87 dependent: set(para_from_vars).
% 1.69/1.87 dependent: set(eq_units_both_ways).
% 1.69/1.87 dependent: set(dynamic_demod_all).
% 1.69/1.87 dependent: set(dynamic_demod).
% 1.69/1.87 dependent: set(order_eq).
% 1.69/1.87 dependent: set(back_demod).
% 1.69/1.87 dependent: set(lrpo).
% 1.69/1.87 dependent: set(hyper_res).
% 1.69/1.87 dependent: clear(order_hyper).
% 1.69/1.87
% 1.69/1.87 ------------> process usable:
% 1.69/1.87 ** KEPT (pick-wt=4): 1 [] theorem(A)| -axiom(A).
% 1.69/1.87 ** KEPT (pick-wt=8): 2 [] theorem(A)| -theorem(implies(B,A))| -theorem(B).
% 1.69/1.87 ** KEPT (pick-wt=12): 3 [] -theorem(e_quivalent(not(implies(not(p),not(q))),and(not(p),q))).
% 1.69/1.87
% 1.69/1.87 ------------> process sos:
% 1.69/1.87 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.69/1.87 ** KEPT (pick-wt=6): 5 [] axiom(implies(or(A,A),A)).
% 1.69/1.87 ** KEPT (pick-wt=6): 6 [] axiom(implies(A,or(B,A))).
% 1.69/1.87 ** KEPT (pick-wt=8): 7 [] axiom(implies(or(A,B),or(B,A))).
% 1.69/1.87 ** KEPT (pick-wt=12): 8 [] axiom(implies(or(A,or(B,C)),or(B,or(A,C)))).
% 1.69/1.87 ** KEPT (pick-wt=12): 9 [] axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))).
% 1.69/1.87 ** KEPT (pick-wt=8): 11 [copy,10,flip.1] or(not(A),B)=implies(A,B).
% 1.69/1.87 ---> New Demodulator: 12 [new_demod,11] or(not(A),B)=implies(A,B).
% 1.69/1.87 ** KEPT (pick-wt=9): 14 [copy,13,demod,12,flip.1] not(implies(A,not(B)))=and(A,B).
% 1.69/1.87 ---> New Demodulator: 15 [new_demod,14] not(implies(A,not(B)))=and(A,B).
% 1.69/1.87 ** KEPT (pick-wt=11): 17 [copy,16,flip.1] and(implies(A,B),implies(B,A))=e_quivalent(A,B).
% 1.69/1.87 ---> New Demodulator: 18 [new_demod,17] and(implies(A,B),implies(B,A))=e_quivalent(A,B).
% 1.69/1.87 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.69/1.87 >>>> Starting back demodulation with 12.
% 1.69/1.87 >>>> Starting back demodulation with 15.
% 1.69/1.87 >> back demodulating 3 with 15.
% 1.69/1.87 >>>> Starting back demodulation with 18.
% 1.69/1.87
% 1.69/1.87 ======= end of input processing =======
% 1.69/1.87
% 1.69/1.87 =========== start of search ===========
% 1.69/1.87
% 1.69/1.87
% 1.69/1.87 Resetting weight limit to 10.
% 1.69/1.87
% 1.69/1.87
% 1.69/1.87 Resetting weight limit to 10.
% 1.69/1.87
% 1.69/1.87 sos_size=153
% 1.69/1.87
% 1.69/1.87 -------- PROOF --------
% 1.69/1.87
% 1.69/1.87 ----> UNIT CONFLICT at 0.01 sec ----> 277 [binary,276.1,19.1] $F.
% 1.69/1.87
% 1.69/1.87 Length of proof is 24. Level of proof is 13.
% 1.69/1.87
% 1.69/1.87 ---------------- PROOF ----------------
% 1.69/1.87 % SZS status Unsatisfiable
% 1.69/1.87 % SZS output start Refutation
% See solution above
% 1.69/1.87 ------------ end of proof -------------
% 1.69/1.87
% 1.69/1.87
% 1.69/1.87 Search stopped by max_proofs option.
% 1.69/1.87
% 1.69/1.87
% 1.69/1.87 Search stopped by max_proofs option.
% 1.69/1.87
% 1.69/1.87 ============ end of search ============
% 1.69/1.87
% 1.69/1.87 -------------- statistics -------------
% 1.69/1.87 clauses given 89
% 1.69/1.87 clauses generated 1578
% 1.69/1.87 clauses kept 269
% 1.69/1.87 clauses forward subsumed 1048
% 1.69/1.87 clauses back subsumed 6
% 1.69/1.87 Kbytes malloced 4882
% 1.69/1.87
% 1.69/1.87 ----------- times (seconds) -----------
% 1.69/1.87 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.69/1.87 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.69/1.87 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.87
% 1.69/1.87 That finishes the proof of the theorem.
% 1.69/1.87
% 1.69/1.87 Process 30378 finished Wed Jul 27 09:42:53 2022
% 1.69/1.87 Otter interrupted
% 1.69/1.87 PROOF FOUND
%------------------------------------------------------------------------------