TSTP Solution File: LCL114-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL114-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:03:36 EDT 2022
% Result : Unsatisfiable 1.89s 2.07s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 5 RR)
% Number of literals : 34 ( 33 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 48 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
implies(implies(x,y),implies(not(y),not(x))) != truth,
file('LCL114-2.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('LCL114-2.p',unknown),
[] ).
cnf(4,axiom,
implies(truth,A) = A,
file('LCL114-2.p',unknown),
[] ).
cnf(5,axiom,
implies(implies(A,B),implies(implies(B,C),implies(A,C))) = truth,
file('LCL114-2.p',unknown),
[] ).
cnf(7,axiom,
implies(implies(A,B),B) = implies(implies(B,A),A),
file('LCL114-2.p',unknown),
[] ).
cnf(8,axiom,
implies(implies(not(A),not(B)),implies(B,A)) = truth,
file('LCL114-2.p',unknown),
[] ).
cnf(10,plain,
implies(implies(implies(A,B),B),A) = implies(implies(A,implies(B,A)),implies(B,A)),
inference(para_into,[status(thm),theory(equality)],[7,7]),
[iquote('para_into,7.1.1.1,7.1.1')] ).
cnf(12,plain,
implies(implies(A,truth),truth) = implies(A,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,4])]),
[iquote('para_into,7.1.1.1,3.1.1,flip.1')] ).
cnf(22,plain,
implies(implies(not(A),not(truth)),A) = truth,
inference(para_into,[status(thm),theory(equality)],[8,4]),
[iquote('para_into,8.1.1.2,3.1.1')] ).
cnf(24,plain,
implies(implies(implies(A,B),implies(not(B),not(A))),implies(not(B),not(A))) = implies(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[8,7]),4])]),
[iquote('para_from,8.1.1,7.1.1.1,demod,4,flip.1')] ).
cnf(28,plain,
implies(implies(implies(A,B),C),implies(implies(not(B),not(A)),C)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,8]),4]),
[iquote('para_into,5.1.1.1,8.1.1,demod,4')] ).
cnf(34,plain,
implies(A,implies(implies(A,B),B)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,4]),4]),
[iquote('para_into,5.1.1.1,3.1.1,demod,4')] ).
cnf(44,plain,
implies(implies(A,truth),implies(B,implies(A,B))) = truth,
inference(para_into,[status(thm),theory(equality)],[5,4]),
[iquote('para_into,5.1.1.2.1,3.1.1')] ).
cnf(74,plain,
implies(implies(A,implies(not(A),not(truth))),implies(not(A),not(truth))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[22,7]),4])]),
[iquote('para_from,22.1.1,7.1.1.1,demod,4,flip.1')] ).
cnf(83,plain,
implies(A,A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,4]),4]),
[iquote('para_into,34.1.1.2.1,3.1.1,demod,4')] ).
cnf(87,plain,
implies(A,truth) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,12]),83]),
[iquote('para_into,34.1.1.2,12.1.1,demod,83')] ).
cnf(91,plain,
implies(A,implies(B,A)) = truth,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),87,4]),
[iquote('back_demod,44,demod,87,4')] ).
cnf(92,plain,
implies(implies(implies(A,B),B),A) = implies(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[10]),91,4]),
[iquote('back_demod,10,demod,91,4')] ).
cnf(120,plain,
implies(implies(A,B),implies(A,implies(C,B))) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[91,5]),4]),
[iquote('para_from,90.1.1,5.1.1.2.1,demod,4')] ).
cnf(130,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[92,22]),4])]),
[iquote('para_into,92.1.1.1,22.1.1,demod,4,flip.1')] ).
cnf(174,plain,
implies(A,implies(B,implies(C,A))) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[120,91]),4]),
[iquote('para_into,120.1.1.1,90.1.1,demod,4')] ).
cnf(206,plain,
implies(not(A),implies(A,B)) = truth,
inference(para_into,[status(thm),theory(equality)],[174,24]),
[iquote('para_into,174.1.1.2,24.1.1')] ).
cnf(231,plain,
implies(not(truth),A) = truth,
inference(para_into,[status(thm),theory(equality)],[206,4]),
[iquote('para_into,206.1.1.2,3.1.1')] ).
cnf(237,plain,
not(not(truth)) = truth,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[130]),231])]),
[iquote('back_demod,130,demod,231,flip.1')] ).
cnf(269,plain,
implies(not(not(A)),A) = truth,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,22]),237,4,4]),
[iquote('para_into,28.1.1.1,22.1.1,demod,237,4,4')] ).
cnf(301,plain,
implies(A,not(not(A))) = truth,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[269,24]),269,87,83])]),
[iquote('para_from,268.1.1,24.1.1.2,demod,269,87,83,flip.1')] ).
cnf(310,plain,
not(not(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[269,7]),4,301,4])]),
[iquote('para_from,268.1.1,7.1.1.1,demod,4,301,4,flip.1')] ).
cnf(321,plain,
implies(A,implies(not(A),B)) = truth,
inference(para_from,[status(thm),theory(equality)],[310,206]),
[iquote('para_from,310.1.1,206.1.1.1')] ).
cnf(333,plain,
implies(not(A),not(truth)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[74]),321,4]),
[iquote('back_demod,74,demod,321,4')] ).
cnf(336,plain,
implies(A,not(truth)) = not(A),
inference(para_into,[status(thm),theory(equality)],[333,310]),
[iquote('para_into,333.1.1.1,310.1.1')] ).
cnf(337,plain,
not(A) = implies(A,not(truth)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[336])]),
[iquote('copy,336,flip.1')] ).
cnf(417,plain,
implies(implies(A,B),implies(not(B),implies(A,not(truth)))) = truth,
inference(para_from,[status(thm),theory(equality)],[336,5]),
[iquote('para_from,336.1.1,5.1.1.2.1')] ).
cnf(435,plain,
truth != truth,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[337,1]),417]),
[iquote('para_from,337.1.1,1.1.1.2.2,demod,417')] ).
cnf(436,plain,
$false,
inference(binary,[status(thm)],[435,2]),
[iquote('binary,435.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL114-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n015.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 09:25:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.89/2.07 ----- Otter 3.3f, August 2004 -----
% 1.89/2.07 The process was started by sandbox2 on n015.cluster.edu,
% 1.89/2.07 Wed Jul 27 09:25:12 2022
% 1.89/2.07 The command was "./otter". The process ID is 18991.
% 1.89/2.07
% 1.89/2.07 set(prolog_style_variables).
% 1.89/2.07 set(auto).
% 1.89/2.07 dependent: set(auto1).
% 1.89/2.07 dependent: set(process_input).
% 1.89/2.07 dependent: clear(print_kept).
% 1.89/2.07 dependent: clear(print_new_demod).
% 1.89/2.07 dependent: clear(print_back_demod).
% 1.89/2.07 dependent: clear(print_back_sub).
% 1.89/2.07 dependent: set(control_memory).
% 1.89/2.07 dependent: assign(max_mem, 12000).
% 1.89/2.07 dependent: assign(pick_given_ratio, 4).
% 1.89/2.07 dependent: assign(stats_level, 1).
% 1.89/2.07 dependent: assign(max_seconds, 10800).
% 1.89/2.07 clear(print_given).
% 1.89/2.07
% 1.89/2.07 list(usable).
% 1.89/2.07 0 [] A=A.
% 1.89/2.07 0 [] implies(truth,X)=X.
% 1.89/2.07 0 [] implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))=truth.
% 1.89/2.07 0 [] implies(implies(X,Y),Y)=implies(implies(Y,X),X).
% 1.89/2.07 0 [] implies(implies(not(X),not(Y)),implies(Y,X))=truth.
% 1.89/2.07 0 [] implies(implies(x,y),implies(not(y),not(x)))!=truth.
% 1.89/2.07 end_of_list.
% 1.89/2.07
% 1.89/2.07 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.89/2.07
% 1.89/2.07 All clauses are units, and equality is present; the
% 1.89/2.07 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.89/2.07
% 1.89/2.07 dependent: set(knuth_bendix).
% 1.89/2.07 dependent: set(anl_eq).
% 1.89/2.07 dependent: set(para_from).
% 1.89/2.07 dependent: set(para_into).
% 1.89/2.07 dependent: clear(para_from_right).
% 1.89/2.07 dependent: clear(para_into_right).
% 1.89/2.07 dependent: set(para_from_vars).
% 1.89/2.07 dependent: set(eq_units_both_ways).
% 1.89/2.07 dependent: set(dynamic_demod_all).
% 1.89/2.07 dependent: set(dynamic_demod).
% 1.89/2.07 dependent: set(order_eq).
% 1.89/2.07 dependent: set(back_demod).
% 1.89/2.07 dependent: set(lrpo).
% 1.89/2.07
% 1.89/2.07 ------------> process usable:
% 1.89/2.07 ** KEPT (pick-wt=11): 1 [] implies(implies(x,y),implies(not(y),not(x)))!=truth.
% 1.89/2.07
% 1.89/2.07 ------------> process sos:
% 1.89/2.07 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.89/2.07 ** KEPT (pick-wt=5): 3 [] implies(truth,A)=A.
% 1.89/2.07 ---> New Demodulator: 4 [new_demod,3] implies(truth,A)=A.
% 1.89/2.07 ** KEPT (pick-wt=13): 5 [] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 1.89/2.07 ---> New Demodulator: 6 [new_demod,5] implies(implies(A,B),implies(implies(B,C),implies(A,C)))=truth.
% 1.89/2.07 ** KEPT (pick-wt=11): 7 [] implies(implies(A,B),B)=implies(implies(B,A),A).
% 1.89/2.07 ** KEPT (pick-wt=11): 8 [] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 1.89/2.07 ---> New Demodulator: 9 [new_demod,8] implies(implies(not(A),not(B)),implies(B,A))=truth.
% 1.89/2.07 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.89/2.07 >>>> Starting back demodulation with 4.
% 1.89/2.07 >>>> Starting back demodulation with 6.
% 1.89/2.07 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] implies(implies(A,B),B)=implies(implies(B,A),A).
% 1.89/2.07 >>>> Starting back demodulation with 9.
% 1.89/2.07
% 1.89/2.07 ======= end of input processing =======
% 1.89/2.07
% 1.89/2.07 =========== start of search ===========
% 1.89/2.07
% 1.89/2.07 -------- PROOF --------
% 1.89/2.07
% 1.89/2.07 ----> UNIT CONFLICT at 0.02 sec ----> 436 [binary,435.1,2.1] $F.
% 1.89/2.07
% 1.89/2.07 Length of proof is 27. Level of proof is 17.
% 1.89/2.07
% 1.89/2.07 ---------------- PROOF ----------------
% 1.89/2.07 % SZS status Unsatisfiable
% 1.89/2.07 % SZS output start Refutation
% See solution above
% 1.89/2.07 ------------ end of proof -------------
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Search stopped by max_proofs option.
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Search stopped by max_proofs option.
% 1.89/2.07
% 1.89/2.07 ============ end of search ============
% 1.89/2.07
% 1.89/2.07 -------------- statistics -------------
% 1.89/2.07 clauses given 28
% 1.89/2.07 clauses generated 784
% 1.89/2.07 clauses kept 223
% 1.89/2.07 clauses forward subsumed 643
% 1.89/2.07 clauses back subsumed 0
% 1.89/2.07 Kbytes malloced 2929
% 1.89/2.07
% 1.89/2.07 ----------- times (seconds) -----------
% 1.89/2.07 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.89/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.89/2.07 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.89/2.07
% 1.89/2.07 That finishes the proof of the theorem.
% 1.89/2.07
% 1.89/2.07 Process 18991 finished Wed Jul 27 09:25:13 2022
% 1.89/2.07 Otter interrupted
% 1.89/2.07 PROOF FOUND
%------------------------------------------------------------------------------